user-1: I am sure everybody in this world thinks that 'my religion is the only true religion' etc and its variables. As we live in a diverse society, in today's age of information we invariably bump into people or places, online or offline, with ideologies which totally contradict Buddhist beliefs.
What is the best strategy to deal with such situations? Should we keep silence and ignore and let them live in their ignorance or should we confront and try to explain the Dhamma to them?
In the latter situation, it always ends up in heated debates about the existence of god and its near impossible to explain a non-Buddhist that soul doesn't exist and that self is an illusion.
What do you do?

user12238: For this answer, I'm going g to draw on a story from a non Buddhist tradition.
There is a Jewish story, that a skeptical passerby asked a very famous Jewish teacher (rabbi) to explain Judaism while standing on one leg. The answer was roughly, "what is hateful/seems wrong (to you) do not do it to others. This is the core, the rest is explanation."
Why do I offer this quote? Because it wasn't necessary to explain about god, or holy people, or specific laws of his religion, or anything else, to give this answer. I am sure that from all the wisdom of Buddhism, you can find a core which will be understood by others. Perhaps "Life is unpredictable and contains sorrow. Buddhism teaches that if you cannot stand aside from the sorrow,when it is your turn, and accept that this is part of the pattern of life, you will develop negative perspectives on life,and those will harm you and other living beings. Therefore, learn to be compassionate and caring for all living beings, for all suffer, and all will one day die." Or whatever wording you prefer.
But you can condense it to a description that most will understand.
Then, after that,anything else,explain that "I personally also believe that.....(other stuff), because my teachers and traditions teach me so."
The key is, the important things about Buddhism will either be able to be said in a way they can appreciate and fit into their tradition, or else it doesn't deter them from Buddhism at the least, because you've made clear they are just your personal beliefs... which they can consider, accept, learn, or sideline as they need to.

user6994: Whether ideas should be confronted to start with depends on the type of idea. It depends on whether they fuel virtue or non-virtue (such as anger, for instance) and it depends on how it leads one to act.
"Black people are lesser than white people" is an idea. "The gods want us to sacrifice goats, and if we do so, we will be able to cross the sea to go back home" is another. It is not hard to see how non-virtuous these ideas are.
In Buddhism, facts matters to the extent that we suffer because we do not see things the way they are (when we conceive of what is impermanent as being permanent... suffering as happiness... impure as pure... empty as having a self, etc), however, being a good Christian is better than being a bad Buddhist.
Hence, the question is not primarily "Is this idea factually concordant or not?" but "Is this idea wholesome and does it lead to wholesome actions or not?". It can also be "Is the way that person relates to this idea wholesome?". This is because it depends as much on the idea as it depends on the way we relate to them.
Anyway, it doesn't answer your question: what is the best strategy?
I think of two of them:
The first is to be an example of virtue, compassion, wisdom, and discipline yourself. It is the best way to inspire others: for them to want to become more like you, without you have to "preach" anything.
The second is to put efforts to build a trust relationship before. Without such a relationship, none will hear what you say to start with.
In any case, you need to be patient, and you need to restrain yourself from speaking to quickly. Take the time to know where she stands first. Take time to hear her instead of assuming from the start.
"Patience" can be a third strategy. Together with humility, it's a good ground for listening and understanding.

user-1: 
Should we keep silence and ignore and let them live in their ignorance or should we confront and try to explain the Dhamma to them?

What comes to my mind is the story of Buddha not really being keen on teaching others.
(From the Pāsarāsi sutta [MN 26].) 

‘Enough with teaching the Dhamma That even I found hard to reach; For
  it will never be perceived By those who live in lust and hate.
Those dyed in lust, wrapped in darkness Will never discern this
  abstruse Dhamma Which goes against the worldly stream, Subtle, deep,
  and difficult to see.’
Considering thus, my mind inclined to inaction rather than to teaching
  the Dhamma. ... '

So, I guess there are several factors.
Is the other person just spouting his/her own opinions and idea's or really open to discussion? Does (s)he want to hear something contrary to own belief?
Of course also relevant: what is your own motivation? Why do you want to confront and explain? Is it truly out of compassion or is it just wanting?
How does trying to convince someone else help you? Does it make your mind peaceful or is it disquieting? 
In my own little world of experience it's is more peaceful to stay out of discussions, opinions, confrontation and so forth.
Hope this helps a bit.

user11524: In my experience, every religion seems to be based on the same deep fondation of widsom. 
The diffences are superficial. Believing in a god for instance should not be considered a bad thing if it helps people to live moraly and to adhere to this wisdom or to pursue it. 
I would only confront people whith their ideas if they take religion as an excuse to do bad things, by encouraging them to reflect on their actions. 
Afterall, there are a lot of people in ths world. Everyone thinks differently and thus a religion that suits you will not and should not suit everyone, that's why there are so many of them.  
So I would say to stay out of the debate as long as it is about the superficial aspects of a religion (aka beliefs), and engage into it only if you feel like people would commit ubskillful actions in the name of it, as something is likely not well understood from their perspective and I am lileky to make a difference without contradicting their beliefs. 

user-1: One of the answers on how do you confront a different religion is that you really don't.
There is no need to confront anything and anyone. Dalai Lama points out that nearly all religions have the same potential, message and goal; the wish to bring the world to better conditions and make humanity more compassionate is shared amongst all of them.
We can all work towards a similar better aim, there isn't any need for elitism and feelings of superiority. We can have fruitful conversations rather than painful quarrels.
From my perspective, apart from my wife, none of the people I know, and especially friends of mine, have a clue that I am a Buddhist. If prompted for an answer all I say is I want to be a better person, and meditate to purify my mind and to be a better human being. That works and serves as a middle ground; we don't have to march out with labels, sings and other things. We can keep that away as signs and labels are distractions, we should go forth beyond them, with no attachment to them, ready to let go of them for greater good.
If Christians feel that there is a soul - fine, I cannot really deny it, although I cannot really find it either, through my own experience. The point being is that it takes to shred ego down to have compassionate possibility and ability of dialogue, to discuss real stuff, rather than going about pillars of doctrine in a dualistic, divisive realm of signs. At that level of discussion it all aims towards the same direction, typically, which is liberation from suffering.

user13820: Telling other people that what they do wrong and even more that what they believe is wrong does not work well. I barely works when supported with facts, but as religion is about belief, it will work even less. It is better to lead by good example and an open discussion. Show similarities and listen to them. I am not confessed to any religion, but I can very well understand how people benefit from a religion when discussing it in such a way instead of more agressive persuasion.

user8157: The actual Buddhist way is to keep silence and ignore and let them live in their manner. The question asked isn't actually an issue in Theravada Buddhism. The Pali teachings literally say to only teach Dhamma to those who are interested and attentive (AN 9.5; MN 26; etc). 
Also, since "self" is an illusion, why would there be any reason for arguments & debates? 

user254: There's an apocryphal Christian story, that I heard or read long ago -- where somebody asks someone else (possibly a Buddhist):


Have you ever thought of becoming a Christian?


... to which the person replies:


If you mean a good Christian, like your Christ -- I don't have the courage.
But if you mean being a bad Christian, like you -- I wouldn't want to be!


If you want to be persuasive (about the benefits and/or truths of Buddhism) perhaps it's important to be a good Buddhist.
I don't want to criticise but "ending up in heated debates about the existence of God" doesn't sound attractive or persuasive to me.
I'm particularly afraid of someone's thinking, "if being a Buddhist means being like you, I wouldn't want to be!"

I once tried to explain Buddhism (not in a "confrontational" way) -- see How to explain what Buddhism is? -- and I don't think I was very successful.
Still I hope I learned from that, that there are many different aspects of Buddhism: and different aspects appeal to or make sense to different people.
The Buddha was especially skilled at knowing different people and speaking accordingly.
It may be that the topics of God, Soul, and Self are especially important to you -- for what it's worth or for example, I don't see that as the most important doctrine.
A friend once told me a bit about communication theory, saying that when people choose a topic of conversation, then talking about what's far away (distant) is less intimate than what's close (here); that what's in the past or future is less intimate than what's now; and that talking about people we don't know, and/or talking about friends, is less intimate than talking about ourselves.
It seems to me that talking about "God" is very distant. Perhaps it's too easy to argue about something you can't see!
If you want to talk about Buddhism maybe it's better to consider aspects of Dharma like Ehipassiko, perhaps like the Kalama sutta.

Five more things.
One is that I tend to assume "good faith".
My parents professed Christianity when I was young. I don't think they were doing that in order to deceive me.
I assume they had some reason[s] for their belief[s] and that the words they spoke had some meaning[s] to them, even if those words didn't wholly make "real" sense to me.
So if I were going to engage in a conversation about God and Soul and so on, I think my participation ought to include my being interested in finding out or understanding what those words mean to someone, and why they use them and so on.1
Conversely, if I'm not interested in doing that, then it's maybe not a topic of conversation I should engage in.
The second is that (when I was young and they were trying to indoctrinate me) I was willing to believe all kinds of doctrines. Or if not believe, at least not dispute. "So, God wants us to love our neighbour as ourself? Well sure, why not. Good doctrine, more or less. And God loves us? That's nice to know, thanks for saying so. And there's a resurrection and an afterlife? Well, OK: if you say so." There was one bit of doctrine though that I couldn't manage. The way it was taught at that time was, "The Church has a monopoly on the Truth: what the Church teaches is true, and everything/everyone else (including every other religion) is wrong." And I thought, that bit of doctrine was just too much: "So, 'the Annunciation', OK, 'the Trinity, Transubstantiation, Purgatory, Heaven' ... whatever, OK: if you say so. But 'everyone else is wrong'? That's incredible! Impossible!" And I think that maybe Buddhism too warns against being a sectarian who argues in this way ("This alone is true") about the dhamma.
The third is that I guess (if you'll excuse my saying so) that your "heated debates" are motivated by some form of conceit, specifically comparing yourself to others: "I'm Buddhist and they're not. My being Buddhist means I know the Dhamma, whereas they are living in ignorance." That's maybe not something you want to perpetuate (even when the debate is whether 'self' is an illusion).
Fourth, if you are arguing online that's maybe even less sensible/effective than face-to-face (xkcd).
Fifth, IMO the "ideologies which totally contradict Buddhist beliefs" are for example the ideologies which involve killing -- or lying, and so on. If you understand that kind of doctrine to be the "bottom line", you might decide most people are agreeable or "very civilized".
1Maybe you can see this sort of attitude here, i.e. I like to assume that I'm at least a little ignorant about another person's views.

-1: <p>I am sure everybody in this world thinks that 'my religion is the only true religion' etc and its variables. As we live in a diverse society, in today's age of information we invariably bump into people or places, online or offline, with ideologies which totally contradict Buddhist beliefs.</p>

<p>What is the best strategy to deal with such situations? Should we keep silence and ignore and let them live in their ignorance or should we confront and try to explain the Dhamma to them?</p>

<p>In the latter situation, it always ends up in heated debates about the existence of god and its near impossible to explain a non-Buddhist that soul doesn't exist and that self is an illusion.</p>

<p>What do you do?</p>
 12238: <p>For this answer, I'm going g to draw on a story from a non Buddhist tradition.</p>

<p>There is a Jewish story, that a skeptical passerby asked a very famous Jewish teacher (rabbi) to explain Judaism while standing on one leg. The answer was roughly, "what is hateful/seems wrong (to you) do not do it to others. This is the core, the rest is explanation."</p>

<p>Why do I offer this quote? Because it wasn't necessary to explain about god, or holy people, or specific laws of his religion, or anything else, to give this answer. I am sure that from all the wisdom of Buddhism, you can find a core which will be understood by others. Perhaps <em>"Life is unpredictable and contains sorrow. Buddhism teaches that if you cannot stand aside from the sorrow,when it is your turn, and accept that this is part of the pattern of life, you will develop negative perspectives on life,and those will harm you and other living beings. Therefore, learn to be compassionate and caring for all living beings, for all suffer, and all will one day die."</em> Or whatever wording you prefer.</p>

<p>But you can condense it to a description that most will understand.</p>

<p><strong>Then</strong>, after that,anything else,explain that <em>"I personally also believe that.....(other stuff), because my teachers and traditions teach me so."</em></p>

<p>The key is, the important things about Buddhism will either be able to be said in a way they can appreciate and fit into their tradition, or else it doesn't deter them from Buddhism at the least, because you've made clear they are just your personal beliefs... which they can consider, accept, learn, or sideline as they need to.</p>
 6994: <p>Whether ideas should be confronted to start with depends on the type of idea. It depends on whether they fuel virtue or non-virtue (such as anger, for instance) and it depends on how it leads one to act.</p>

<p>"Black people are lesser than white people" is an idea. "The gods want us to sacrifice goats, and if we do so, we will be able to cross the sea to go back home" is another. It is not hard to see how non-virtuous these ideas are.</p>

<p>In Buddhism, facts matters to the extent that we suffer because we do not see things the way they are (when we conceive of what is impermanent as being permanent... suffering as happiness... impure as pure... empty as having a self, etc), however, being a good Christian is better than being a bad Buddhist.</p>

<p>Hence, the question is not primarily "Is this idea factually concordant or not?" but "Is this idea wholesome and does it lead to wholesome actions or not?". It can also be "Is the way that person relates to this idea wholesome?". This is because it depends as much on the idea as it depends on the way we relate to them.</p>

<p>Anyway, it doesn't answer your question: what is the best strategy?</p>

<p>I think of two of them:</p>

<p>The first is to be an example of virtue, compassion, wisdom, and discipline yourself. It is the best way to inspire others: for them to want to become more like you, without you have to "preach" anything.</p>

<p>The second is to put efforts to build a trust relationship before. Without such a relationship, none will hear what you say to start with.</p>

<p>In any case, you need to be patient, and you need to restrain yourself from speaking to quickly. Take the time to know where she stands first. Take time to hear her instead of assuming from the start.</p>

<p>"Patience" can be a third strategy. Together with humility, it's a good ground for listening and understanding.</p>
 -1: <blockquote>
  <p>Should we keep silence and ignore and let them live in their ignorance or should we confront and try to explain the Dhamma to them?</p>
</blockquote>

<p>What comes to my mind is the story of Buddha not really being keen on teaching others.
(From the <a href="https://suttacentral.net/mn26/en/bodhi" rel="nofollow noreferrer">Pāsarāsi sutta</a> [MN 26].) </p>

<blockquote>
  <p>‘Enough with teaching the Dhamma That even I found hard to reach; For
  it will never be perceived By those who live in lust and hate.</p>
  
  <p>Those dyed in lust, wrapped in darkness Will never discern this
  abstruse Dhamma Which goes against the worldly stream, Subtle, deep,
  and difficult to see.’</p>
  
  <p>Considering thus, my mind inclined to inaction rather than to teaching
  the Dhamma. ... '</p>
</blockquote>

<p>So, I guess there are several factors.
Is the other person just spouting his/her own opinions and idea's or really open to discussion? Does (s)he want to hear something contrary to own belief?
Of course also relevant: what is your own motivation? Why do you want to confront and explain? Is it truly out of compassion or is it just wanting?
How does trying to convince someone else help you? Does it make your mind peaceful or is it disquieting? </p>

<p>In my own little world of experience it's is more peaceful to stay out of discussions, opinions, confrontation and so forth.</p>

<p>Hope this helps a bit.</p>
 11524: <p>In my experience, every religion seems to be based on the same deep fondation of widsom. </p>

<p>The diffences are superficial. Believing in a god for instance should not be considered a bad thing if it helps people to live moraly and to adhere to this wisdom or to pursue it. </p>

<p>I would only confront people whith their ideas if they take religion as an excuse to do bad things, by encouraging them to reflect on their actions. </p>

<p>Afterall, there are a lot of people in ths world. Everyone thinks differently and thus a religion that suits you will not and should not suit everyone, that's why there are so many of them.  </p>

<p>So I would say to stay out of the debate as long as it is about the superficial aspects of a religion (aka beliefs), and engage into it only if you feel like people would commit ubskillful actions in the name of it, as something is likely not well understood from their perspective and I am lileky to make a difference without contradicting their beliefs. </p>
 -1: <p>One of the answers on how do you confront a different religion is that <em>you really <strong>don't</em></strong>.</p>

<p>There is no need to confront anything and anyone. Dalai Lama points out that nearly all religions have the same potential, message and goal; the wish to bring the world to better conditions and make humanity more compassionate is shared amongst all of them.</p>

<p>We can all work towards a similar better aim, there isn't any need for elitism and feelings of superiority. We can have fruitful conversations rather than painful quarrels.</p>

<p>From my perspective, apart from my wife, none of the people I know, and especially friends of mine, have a clue that I am a Buddhist. If prompted for an answer all I say is I want to be a better person, and meditate to purify my mind and to be a better human being. That works and serves as a middle ground; we don't have to march out with labels, sings and other things. We can keep that away as signs and labels are distractions, we should go forth beyond them, with no attachment to them, ready to let go of them for greater good.</p>

<p>If Christians feel that there is a soul - fine, I cannot <em>really</em> deny it, although I cannot really find it either, through my own experience. The point being is that it takes to shred ego down to have compassionate possibility and ability of dialogue, to discuss real stuff, rather than going about pillars of doctrine in a dualistic, divisive realm of signs. At that level of discussion it all aims towards the same direction, typically, which is liberation from suffering.</p>
 13820: <p>Telling other people that what they do wrong and even more that what they believe is wrong does not work well. I barely works when supported with facts, but as religion is about belief, it will work even less. It is better to lead by good example and an open discussion. Show similarities and listen to them. I am not confessed to any religion, but I can very well understand how people benefit from a religion when discussing it in such a way instead of more agressive persuasion.</p>
 8157: <p>The actual Buddhist way is to keep silence and ignore and let them live in their manner. The question asked isn't actually an issue in Theravada Buddhism. The Pali teachings literally say to only teach Dhamma to those who are interested and attentive (AN 9.5; MN 26; etc). </p>

<p>Also, since "self" is an illusion, why would there be any reason for arguments &amp; debates? </p>
 254: <p>There's an apocryphal Christian story, that I heard or read long ago -- where somebody asks someone else (possibly a Buddhist):</p>

<blockquote>
  <ul>
  <li>Have you ever thought of becoming a Christian?</li>
  </ul>
</blockquote>

<p>... to which the person replies:</p>

<blockquote>
  <ul>
  <li><p>If you mean a <em>good</em> Christian, like your Christ -- I don't have the courage.</p>
  
  <p>But if you mean being a <em>bad</em> Christian, like you -- I wouldn't want to be!</p></li>
  </ul>
</blockquote>

<p>If you want to be persuasive (about the benefits and/or truths of Buddhism) perhaps it's important to be a good Buddhist.</p>

<p>I don't want to criticise but "ending up in heated debates about the existence of God" doesn't sound attractive or persuasive to me.</p>

<p>I'm particularly afraid of someone's thinking, "if being a Buddhist means being like <em>you</em>, I wouldn't want to be!"</p>

<hr>

<p>I once tried to explain Buddhism (not in a "confrontational" way) -- see <a href="https://buddhism.stackexchange.com/q/7258/254">How to explain what Buddhism is?</a> -- and I don't think I was very successful.</p>

<p>Still I hope I learned from that, that there are many different aspects of Buddhism: and different aspects appeal to or make sense to different people.</p>

<p>The Buddha was especially skilled at knowing different people and speaking accordingly.</p>

<p>It may be that the topics of God, Soul, and Self are especially important to you -- for what it's worth or for example, I don't see that as <a href="https://buddhism.stackexchange.com/a/28313/254">the most important doctrine</a>.</p>

<p>A friend once told me a bit about communication theory, saying that when people choose a topic of conversation, then talking about what's far away (distant) is less intimate than what's close (here); that what's in the past or future is less intimate than what's now; and that talking about people we don't know, and/or talking about friends, is less intimate than talking about ourselves.</p>

<p>It seems to me that talking about "God" is very distant. Perhaps it's too easy to argue about something you can't see!</p>

<p>If you want to talk about Buddhism maybe it's better to consider aspects of Dharma like <a href="https://dhammawiki.com/index.php/Dhamma#The_Six_Qualities_of_The_Dhamma" rel="nofollow noreferrer">Ehipassiko</a>, perhaps like the <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.065.than.html" rel="nofollow noreferrer">Kalama sutta</a>.</p>

<hr>

<p>Five more things.</p>

<p>One is that I tend to assume "good faith".
My parents professed Christianity when I was young. I don't think they were doing that in order to deceive me.
I assume they had some reason[s] for their belief[s] and that the words they spoke had some meaning[s] to them, even if those words didn't wholly make "real" sense to me.
So if I were going to engage in a conversation about God and Soul and so on, I think my participation ought to include my being interested in finding out or understanding what those words <em>mean</em> to someone, and <em>why</em> they use them and so on.<sup><strong>1</strong></sup>
Conversely, if I'm not interested in doing that, then it's maybe not a topic of conversation I should engage in.</p>

<p>The second is that (when I was young and they were trying to indoctrinate me) I was willing to believe all kinds of doctrines. Or if not believe, at least not dispute. "So, God wants us to love our neighbour as ourself? Well sure, why not. Good doctrine, more or less. And God loves us? That's nice to know, thanks for saying so. And there's a resurrection and an afterlife? Well, OK: if you say so." There was one bit of doctrine though that I couldn't manage. The way it was taught at that time was, "The Church has a monopoly on the Truth: what the Church teaches is true, and everything/everyone else (including every other religion) is wrong." And I thought, <em>that</em> bit of doctrine was just too much: "So, 'the Annunciation', OK, 'the Trinity, Transubstantiation, Purgatory, Heaven' ... whatever, OK: if you say so. But 'everyone else is wrong'? That's incredible! Impossible!" And I think that maybe Buddhism too warns against being <a href="https://www.accesstoinsight.org/tipitaka/kn/ud/ud.6.04.than.html" rel="nofollow noreferrer">a sectarian</a> who argues in this way ("This alone is true") about the dhamma.</p>

<p>The third is that I guess (if you'll excuse my saying so) that your "heated debates" are motivated by some form of <a href="https://buddhism.stackexchange.com/q/9415/254">conceit</a>, specifically comparing yourself to others: "I'm Buddhist and they're not. My being Buddhist means I know the Dhamma, whereas they are living in ignorance." That's maybe not something you want to perpetuate (even when the debate is whether 'self' is an illusion).</p>

<p>Fourth, if you are arguing online that's maybe even less sensible/effective than face-to-face (<a href="https://xkcd.com/386/" rel="nofollow noreferrer">xkcd</a>).</p>

<p>Fifth, IMO the "ideologies which totally contradict Buddhist beliefs" are for example the ideologies which involve killing -- or lying, and so on. If you understand that kind of doctrine to be the "bottom line", you might decide most people are agreeable or "<a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.088.than.html" rel="nofollow noreferrer">very civilized</a>".</p>

<p><sup><strong>1</strong></sup><sub>Maybe you can see this sort of attitude <a href="https://buddhism.stackexchange.com/questions/3420/is-rebirth-a-delusional-belief#comment4315_3420">here</a>, i.e. I like to assume that I'm at least a little ignorant about another person's views.</sub></p>
