user-1: If you have doubts on whether your practice (i.e. of the Eightfold Path) will free anyone from saṁsāra in your lifetime, then what reasons can you give for why your practice should take precedence over anything else, namely, alleviating the suffering of others in whatever mundane way you can (even if it does not free anyone from saṁsāra, (e.g. ordinary acts of charity, career in public service, etc.))?

user254: If you have doubts on whether your practice will free anyone from saṁsāra in your lifetime
Is this an example of an aphorism "the perfect is the enemy of the good" -- which, Wikipedia says, is related to a "Nirvana fallacy" -- i.e. "if you can't be perfect, then no point trying to be good"?
what reasons can you give for why your practice should take precedence over anything else
You probably didn't mean it this way, but "precedence over anything else" may be an exaggeration -- for example it's also important (fundamental) to be harmless.
An example (of your being "harmless") is keeping the four or five precepts.
But perhaps this is part of your practice already.
I think it's generally a mistake to assume that dhamma is only one thing (see also here) -- to assume that you can summarise it as one thing, and ignore everything else.
I think that a generosity too is beneficial, not (or not only) for the sake of "helping others" but (perhaps more importantly for "your practice") for the sake of reducing attachment --  or practising non-attachment -- e.g. a material gift may be a small antidote to a self-view that "this is mine".
Personally I think that a great (or greatest) "gift" (that you can give) is not only dhamma (doctrine) but liberation or liberty -- or at least, help provide an environment in which someone can discover/experience (live) liberty. Perhaps you might read the Therigathas -- many of which praise mutti (in comparison to the life they had previously). Some (many) people feel they must seek seclusion, perhaps the homeless life, to be free -- which I think includes being free of evil or unwise company, free of other people's unreasonable demands and expectations, etc. IMO you might extend this gift towards monastics (by helping to support them materially) and towards laypeople (by being undemanding).
So if "your own practice" results in your own behaviour being a bit less "needy"; skilfully abandoning cravings and attachments; maybe having a better of identity (and so for example not, "he is mine" and "she is mine", and "they owe me") -- maybe that helps to answer your question.
In other words I suppose I'd answer that any of your practice is also important towards liberating others, partly because it's (only) because you practice that you're able to help free others.
Also I find it hard to blame the behaviour described in e.g. A messiah for India's abandoned sick -- that (although not explicitly Buddhist) seems to me a practice for cessation of suffering -- for example as described in the Bikkhuni sutta:

There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.

Perhaps you shouldn't assume it's an "either/or" decision (i.e., 'either' your practice 'or' alleviating the suffering of others in whatever mundane way you can) -- perhaps an ideal is 'both', a middle way, a doing one by (or while) doing the other -- or one and the other at different times, like walking with the left foot and the right foot.
Also I think that a Buddhist doctrine which says that you don't give material/mundane aid, and/or that immaterial aid is superior, is intended for monks -- who (by their poverty) have a limit to the type of aid that they're able to give (e.g. they can't give money because they don't possess any) -- but who nevertheless ought to know that what they do have (i.e. Dhamma) and can give is important, worthwhile, worth offering, and superior. I think that the expectations or advice (re. generosity) for lay people is slightly different.

user-1: Because outer peace begins with inner peace. The Buddha said, 

“Monks, there are these four kinds of persons found existing in the world. What four? (1) One who is practicing neither for his own welfare nor for the welfare of others; (2) one who is practicing for the welfare of others but not for his own welfare; (3) one who is practicing for his own welfare but not for the welfare of others; and (4) one who is practicing both for his own welfare and for the welfare of others. 
...
The person practicing for his own welfare but not for the welfare of
  others is the more excellent and sublime of the [first] three persons.
  The person practicing both for his own welfare and for the welfare of
  others is the foremost, the best, the preeminent, the supreme, and the
  finest of these four persons...” (AN 4:95, NDB 476–77)

Hence, the Buddha ordered (3) > (2).

I found the following quote useful in seeing this another way,

We are tied together in the single garment of destiny, caught in an inescapable network of mutuality. And whatever affects one directly affects all indirectly. For some strange reason I can never be what I ought to be until you are what you ought to be. And you can never be what you ought to be until I am what I ought to be. 
King, Martin Luther, Jr. 

and I thought this final quote helped to further see this,

I will protect others,’ bhikkhus: thus should the establishments of mindfulness be practised. Protecting oneself, bhikkhus, one protects others; protecting others, one protects oneself.
“And how is it, bhikkhus, that by protecting oneself one protects others? By the pursuit, development, and cultivation of the four establishments of mindfulness. It is in such a way that by protecting oneself one protects others.
“And how is it, bhikkhus, that by protecting others one protects oneself? By patience, harmlessness, lovingkindness, and sympathy. It is in such a way that by protecting others one protects oneself.
SN 47.19


user471: Generosity, kind words and helpfulness are all meaningful in Buddhism, however small. Every Buddhist and non-Buddhist should practise it. See the next 3 quotes from the suttas.
From Vaccha Sutta:

"I tell you, Vaccha, even if a person throws the rinsings of a bowl or
  a cup into a village pool or pond, thinking, 'May whatever animals
  live here feed on this,' that would be a source of merit, to say
  nothing of what is given to human beings. But I do say that what is
  given to a virtuous person is of great fruit, and not so much what is
  given to an unvirtuous person.

From Itivuttaka 26:

This was said by the Blessed One, said by the Arahant, so I have
  heard: "If beings knew, as I know, the results of giving & sharing,
  they would not eat without having given, nor would the stain of
  selfishness overcome their minds. Even if it were their last bite,
  their last mouthful, they would not eat without having shared, if
  there were someone to receive their gift. But because beings do not
  know, as I know, the results of giving & sharing, they eat without
  having given. The stain of selfishness overcomes their minds."

From Itivuttaka 75:

"And how is a person one who rains everywhere? There is the case where
  a person gives food, drink, clothing, vehicles, garlands, scents,
  ointments, beds, dwellings, & lights to all brahmans & contemplatives,
  to all of the miserable, the homeless, & beggars. This is how a person
  one who rains everywhere.
A person responsive to requests,
  sympathetic to all beings,
  delighting in distributing alms:
  "Give to them! Give!" he says.
  As a cloud — resounding, thundering — rains,
  filling with water, drenching
  the plateaus & gullies:
  a person like this is like that.
  Having rightly amassed wealth
  attained through initiative,
  he satisfies fully with food & drink
  those fallen into the homeless state.

The next quote from Iti 100 however shows something different. It says that the gift of the Dhamma (Buddha's teachings) is superior to all other types of gifts.
From Itivuttaka 100:

"There are these two kinds of gifts: a gift of material things & a
  gift of the Dhamma. Of the two, this is supreme: a gift of the Dhamma.
"There are these two kinds of sharing: sharing of material things &
  sharing of the Dhamma. Of the two, this is supreme: sharing of the
  Dhamma.
"There are these two kinds of assistance: assistance with material
  things & assistance with the Dhamma. Of the two, this is supreme: help
  with the Dhamma.
"There are these two kinds of mass-donations: a mass-donation of
  material things & a mass-donation of the Dhamma. Of the two, this is
  supreme: a mass-donation of the Dhamma."

Why is this the case? Other types of gifts relieve one's sufferings temporarily. But with the Dhamma, even if one would not become free from samsara in this lifetime, it would still guide them (and us) to cleanse our mind, and at least bring us to happy destinations both in this lifetime and the next.
For according to Dhammapada 1:

"All mental phenomena have mind as their forerunner; they have mind as
  their chief; they are mind-made. If one speaks or acts with an evil
  mind, suffering follows him just as the wheel follows the hoofprint of
  the ox that draws the cart."

So, even if learning the Dhamma does not free one from samsara in this lifetime, at least it will guide them to be more skillful mentally. Since the mind is the forerunner to all types of sufferings (see MN 135), becoming skillful in mind, will reduce all sufferings in future.
And according to AN 3.99:

'Now, a trifling evil act done by what sort of individual is
  experienced in the here & now, and for the most part barely appears
  for a moment? There is the case where a certain individual is
  developed in the body, developed in virtue, developed in mind
  [i.e., painful feelings cannot invade the mind and stay there],
  developed in discernment: unrestricted, large-hearted, dwelling with
  the immeasurable. A trifling evil act done by this sort of individual
  is experienced in the here & now, and for the most part barely appears
  for a moment.

This shows how one could reduce his or her suffering by becoming developed in body, virtue and mind.

-1: <p>If you have doubts on whether your practice (i.e. of the Eightfold Path) will free anyone from saṁsāra in your lifetime, then what reasons can you give for why your practice should take precedence over anything else, namely, alleviating the suffering of others in whatever mundane way you can (even if it does not free anyone from saṁsāra, (e.g. ordinary acts of charity, career in public service, etc.))?</p>
 254: <p><strong>If you have doubts on whether your practice will free anyone from saṁsāra in your lifetime</strong></p>

<p>Is this an example of an aphorism "the perfect is the enemy of the good" -- which, Wikipedia says, is related to a "<a href="https://en.wikipedia.org/wiki/Nirvana_fallacy" rel="nofollow noreferrer">Nirvana fallacy</a>" -- i.e. "if you can't be perfect, then no point trying to be good"?</p>

<p><strong>what reasons can you give for why your practice should take precedence over anything else</strong></p>

<p>You probably didn't mean it this way, but "precedence over <em>anything</em> else" may be an exaggeration -- for example it's also important (fundamental) to be harmless.
An example (of your being "harmless") is keeping the four or five precepts.
But perhaps this is part of your practice already.</p>

<p>I think it's generally a mistake to assume that dhamma is only one thing (<a href="https://discourse.suttacentral.net/t/did-the-buddha-only-teach-dukkha-and-its-cessation/9357" rel="nofollow noreferrer">see also here</a>) -- to assume that you can summarise it as one thing, and ignore everything else.</p>

<p>I think that a generosity too is beneficial, not (or not only) for the sake of "helping others" but (perhaps more importantly for "your practice") for the sake of reducing attachment --  or practising non-attachment -- e.g. a material gift may be a small antidote to a self-view that "this is mine".</p>

<p>Personally I think that a great (or greatest) "gift" (that you can give) is not only dhamma (doctrine) but liberation or liberty -- or at least, help provide an environment in which someone can discover/experience (live) liberty. Perhaps you might read the Therigathas -- many of which praise <a href="https://suttacentral.net/define/mutti" rel="nofollow noreferrer">mutti</a> (in comparison to the life they had previously). Some (many) people feel they must seek seclusion, perhaps the homeless life, to be free -- which I think includes being free of evil or unwise company, free of other people's unreasonable demands and expectations, etc. IMO you might extend this gift towards monastics (by helping to support them materially) and towards laypeople (by being undemanding).</p>

<p>So if "your own practice" results in your own behaviour being a bit less "needy"; skilfully abandoning cravings and attachments; maybe having a better of identity (and so for example not, "he is mine" and "she is mine", and "they owe me") -- maybe that helps to answer your question.</p>

<p>In other words I suppose I'd answer that any of your practice is also important towards liberating others, partly because it's (only) because you practice that you're able to help free others.</p>

<p>Also I find it hard to blame the behaviour described in e.g. <a href="https://www.bbc.co.uk/news/world-asia-india-35299545" rel="nofollow noreferrer">A messiah for India's abandoned sick</a> -- that (although not explicitly Buddhist) seems to me a practice for cessation of suffering -- for example as described in the <a href="https://www.accesstoinsight.org/tipitaka/an/an04/an04.159.than.html" rel="nofollow noreferrer">Bikkhuni sutta</a>:</p>

<blockquote>
  <p>There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival &amp; continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, &amp; live in comfort.</p>
</blockquote>

<p>Perhaps you shouldn't assume it's an "either/or" decision (i.e., 'either' your practice 'or' alleviating the suffering of others in whatever mundane way you can) -- perhaps an ideal is 'both', a middle way, a doing one by (or while) doing the other -- or one and the other at different times, like walking with the left foot and the right foot.</p>

<p>Also I think that a Buddhist doctrine which says that you don't give material/mundane aid, and/or that immaterial aid is superior, is intended for monks -- who (by their poverty) have a limit to the type of aid that they're able to give (e.g. they can't give money because they don't possess any) -- but who nevertheless ought to know that what they do have (i.e. Dhamma) and can give is important, worthwhile, worth offering, and superior. I think that the expectations or advice (re. generosity) for lay people is slightly different.</p>
 -1: <p>Because outer peace begins with inner peace. The Buddha said, </p>

<blockquote>
  <p>“Monks, there are these four kinds of persons found existing in the world. What four? (1) One who is practicing neither for his own welfare nor for the welfare of others; (2) one who is practicing for the welfare of others but not for his own welfare; (3) one who is practicing for his own welfare but not for the welfare of others; and (4) one who is practicing both for his own welfare and for the welfare of others. </p>
  
  <p>...</p>
  
  <p>The person practicing for his own welfare but not for the welfare of
  others is the more excellent and sublime of the [first] three persons.
  The person practicing both for his own welfare and for the welfare of
  others is the foremost, the best, the preeminent, the supreme, and the
  finest of these four persons...” (AN 4:95, NDB 476–77)</p>
</blockquote>

<p>Hence, the Buddha ordered <code>(3)</code> > <code>(2)</code>.</p>

<hr>

<p>I found the following quote useful in seeing this another way,</p>

<blockquote>
  <p>We are tied together in the single garment of destiny, caught in an inescapable network of mutuality. And whatever affects one directly affects all indirectly. For some strange reason <strong>I can never be what I ought to be until you are what you ought to be. And you can never be what you ought to be until I am what I ought to be.</strong>  </p>
  
  <p><a href="https://kinginstitute.stanford.edu/king-papers/publications/knock-midnight-inspiration-great-sermons-reverend-martin-luther-king-jr-10" rel="nofollow noreferrer">King, Martin Luther, Jr.</a> </p>
</blockquote>

<p>and I thought this final quote helped to further see this,</p>

<blockquote>
  <p>I will protect others,’ bhikkhus: thus should the establishments of mindfulness be practised. <strong>Protecting oneself, bhikkhus, one protects others; protecting others, one protects oneself.</strong></p>
  
  <p>“And how is it, bhikkhus, that by protecting oneself one protects others? By the pursuit, development, and cultivation of the four establishments of mindfulness. It is in such a way that by protecting oneself one protects others.</p>
  
  <p>“And how is it, bhikkhus, that by protecting others one protects oneself? By patience, harmlessness, lovingkindness, and sympathy. It is in such a way that by protecting others one protects oneself.</p>
  
  <p><a href="https://suttacentral.net/sn47.19/en/bodhi" rel="nofollow noreferrer">SN 47.19</a></p>
</blockquote>
 471: <p>Generosity, kind words and helpfulness are all meaningful in Buddhism, however small. Every Buddhist and non-Buddhist should practise it. See the next 3 quotes from the suttas.</p>

<p>From <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.057.than.html" rel="nofollow noreferrer">Vaccha Sutta</a>:</p>

<blockquote>
  <p>"I tell you, Vaccha, even if a person throws the rinsings of a bowl or
  a cup into a village pool or pond, thinking, 'May whatever animals
  live here feed on this,' that would be a source of merit, to say
  nothing of what is given to human beings. But I do say that what is
  given to a virtuous person is of great fruit, and not so much what is
  given to an unvirtuous person.</p>
</blockquote>

<p>From <a href="https://www.accesstoinsight.org/tipitaka/kn/iti/iti.1.001-027.than.html#iti-026" rel="nofollow noreferrer">Itivuttaka 26</a>:</p>

<blockquote>
  <p>This was said by the Blessed One, said by the Arahant, so I have
  heard: "If beings knew, as I know, the results of giving &amp; sharing,
  they would not eat without having given, nor would the stain of
  selfishness overcome their minds. Even if it were their last bite,
  their last mouthful, they would not eat without having shared, if
  there were someone to receive their gift. But because beings do not
  know, as I know, the results of giving &amp; sharing, they eat without
  having given. The stain of selfishness overcomes their minds."</p>
</blockquote>

<p>From <a href="https://www.accesstoinsight.org/tipitaka/kn/iti/iti.3.050-099.than.html#iti-075" rel="nofollow noreferrer">Itivuttaka 75</a>:</p>

<blockquote>
  <p>"And how is a person one who rains everywhere? There is the case where
  a person gives food, drink, clothing, vehicles, garlands, scents,
  ointments, beds, dwellings, &amp; lights to all brahmans &amp; contemplatives,
  to all of the miserable, the homeless, &amp; beggars. This is how a person
  one who rains everywhere.</p>
  
  <p>A person responsive to requests,<br>
  sympathetic to all beings,<br>
  delighting in distributing alms:<br>
  "Give to them! Give!" he says.<br>
  As a cloud — resounding, thundering — rains,<br>
  filling with water, drenching<br>
  the plateaus &amp; gullies:<br>
  a person like this is like that.<br>
  Having rightly amassed wealth<br>
  attained through initiative,<br>
  he satisfies fully with food &amp; drink<br>
  those fallen into the homeless state.</p>
</blockquote>

<p>The next quote from Iti 100 however shows something different. It says that the gift of the Dhamma (Buddha's teachings) is superior to all other types of gifts.</p>

<p>From <a href="https://www.accesstoinsight.org/tipitaka/kn/iti/iti.4.100-112.than.html#iti-100" rel="nofollow noreferrer">Itivuttaka 100</a>:</p>

<blockquote>
  <p>"There are these two kinds of gifts: a gift of material things &amp; a
  gift of the Dhamma. Of the two, this is supreme: a gift of the Dhamma.</p>
  
  <p>"There are these two kinds of sharing: sharing of material things &amp;
  sharing of the Dhamma. Of the two, this is supreme: sharing of the
  Dhamma.</p>
  
  <p>"There are these two kinds of assistance: assistance with material
  things &amp; assistance with the Dhamma. Of the two, this is supreme: help
  with the Dhamma.</p>
  
  <p>"There are these two kinds of mass-donations: a mass-donation of
  material things &amp; a mass-donation of the Dhamma. Of the two, this is
  supreme: a mass-donation of the Dhamma."</p>
</blockquote>

<p>Why is this the case? Other types of gifts relieve one's sufferings temporarily. But with the Dhamma, even if one would not become free from samsara in this lifetime, it would still guide them (and us) to cleanse our mind, and at least bring us to happy destinations both in this lifetime and the next.</p>

<p>For according to <a href="https://www.tipitaka.net/tipitaka/dhp/verseload.php?verse=001" rel="nofollow noreferrer">Dhammapada 1</a>:</p>

<blockquote>
  <p>"All mental phenomena have mind as their forerunner; they have mind as
  their chief; they are mind-made. If one speaks or acts with an evil
  mind, suffering follows him just as the wheel follows the hoofprint of
  the ox that draws the cart."</p>
</blockquote>

<p>So, even if learning the Dhamma does not free one from samsara in this lifetime, at least it will guide them to be more skillful mentally. Since the mind is the forerunner to all types of sufferings (see <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.135.than.html" rel="nofollow noreferrer">MN 135</a>), becoming skillful in mind, will reduce all sufferings in future.</p>

<p>And according to <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.099.than.html" rel="nofollow noreferrer">AN 3.99</a>:</p>

<blockquote>
  <p>'Now, a trifling evil act done by what sort of individual is
  experienced in the here &amp; now, and for the most part barely appears
  for a moment? There is the case where a certain individual is
  developed in the body, developed in virtue, developed in mind
  [i.e., painful feelings cannot invade the mind and stay there],
  developed in discernment: unrestricted, large-hearted, dwelling with
  the immeasurable. A trifling evil act done by this sort of individual
  is experienced in the here &amp; now, and for the most part barely appears
  for a moment.</p>
</blockquote>

<p>This shows how one could reduce his or her suffering by becoming developed in body, virtue and mind.</p>
