user17322: I happen to read this text from the Buddhist Catechism (which was written by Olcott, published 1881):

Q. What striking contrasts are there between Buddhism and what may be properly called "religions?"
A. Among others, these: It teaches the highest goodness without a creating God; a continuity of life without adhering to the superstitious and selfish doctrine of an eternal, metaphysical soul-substance that goes out of the body; a happiness without an objective heaven; a method of salvation without a vicarious Savior; redemption by oneself as the Redeemer, and without rites, prayers, penances, priests or intercessory saints; and a summun bonum, i.e., Nirvâṇa, attainable in this life and in this world by leading a pure, unselfish life of wisdom and compassion to all beings.

But any recent texts I read about Buddhism all make it appear as if Buddhism is no different from any other dogmatic religion. I understand that Buddhism also underwent a lot of changes due to local cultures and competition from other religions.
What I want to learn is the original core message of Buddhism before it was made into a religion. Where can I find texts for understand this message.

user16489: Below is the core of buddhism which extracted from Saccabihanga sutta

"What is meant by not getting what one desires, that too is suffering?
  To beings subject to birth there comes desire: 'O might we not be
  subject to birth, and birth not come to us.' But this cannot be
  attained by mere desiring. So not getting what one desires, that too,
  is suffering. To beings subject to aging there comes the desire: 'O
  might we not be subject to aging, and aging not come to us...' (as
  before). To beings subject to disease there comes the desire: 'O might
  we not be subject to disease and disease not come to us...' To beings
  subject to death there comes the desire: 'O might we not be subject to
  death and death not come to us...' To beings subject to sorrow,
  lamentation, suffering, misery, and despair there comes the desire: 'O
  might we not be subject to sorrow, lamentation, suffering, misery, and
  despair, and sorrow, lamentation, suffering, misery, and despair not
  come to us.' But this cannot be attained by merely desiring. So not
  getting what one desires that too is suffering.

But in above translation it is written with the word too (that too1 is suffering). But in pali cannon there's nothing like that. It just say, not getting what one desires (yampiccan na labhathi thampi dukkhan). The equal meaning to this in english would be insatiable meaning.
This is the core of the real buddhism, once you understand then you will get a complete different picture about noble truths, dependent origination etc..
And one other correction should be, above explanation is given thinking jathi as birth of living beings, jara as aging of living beings. But that's not 100% correct, in dhamma what is highlighted as birth jathi is the birth of thoughts (good and bad both). And when you are in the right track you will get more wider picture on this. It's bit hard to explain here. If you are interested visit the this website. 
Due to the most of the misguided people this real dhamma is hidden. That's the nature of it. That's why it says Buddha is a very rear person who comes to the world only once for a long long time period. And exposed the reality (dhamma) of this world, which only buddha can be realised without help of anyone. So no need to worry about that.
NOTE: Interesting question from someone who really wants / tries to understand the buddha's message. This answer might be down voted as it doesn't understand by the majority in this forum. Anyway I wrote it though I'm to be given down votes as it seems you are seeking the truth of the world.

user14789: 
a method of salvation without a vicarious Savior;

this is not false, but people need a buddha to hear about the dhamma, which can be seen as a revelation, like when there is some prophet revealing some teaching to people.
For instance the people who keep saying that ''mediation is enough'' to be enlightened are competently wrong.
Even if people were skilled at whatever samadhi they cultivate,  they would fail be enlightened, since they did not hear about the dhamma and then investigate  for themselves the cause of the arising of dukkha and the cause of the cessation of dukkha.
Anyway, since there was always a vinaya and some bikkhus told by the buddha how to live and what rules to follow, it can be said that that the dhamma is a religion, at least for the bikkhus.
But since there is not what people crave the most, ie  cults, rituals, arts, entertainment, symbols, philosophy, as meritorious activities, even less for enlightenment, you can say that the dhamma is not religion, especially for lay people.
Currently people do not talk about pre-religion buddhism and post religious. They talk about pre-sectarian buddhism and post-sectarian buddhism, which is taken to mean before and after some council long time ago, eg after the 2nd council.

For the oldest texts which are easily available in english, it would be as usual the texts in pali,  ie some texts from this long list

and in more details here
https://en.wikipedia.org/wiki/Early_Buddhist_Texts
https://en.wikipedia.org/wiki/Gandh%C4%81ran_Buddhist_texts
https://en.wikipedia.org/wiki/Early_Buddhist_schools

user-1: It seems to me the question is based on false premises. 
But any recent texts I read about Buddhism all make it appear as if Buddhism is no different from any other dogmatic religion. I understand that Buddhism also underwent a lot of changes due to local cultures and competition from other religions.
I don't know what you've read but I have never found a text suggesting Buddhism is a dogmatic religion unless it was written by as sceptical person with no knowledge. 
There have been changes and the teachings will continue to be represented, repackaged and re-explained to suit the times, but the message has not changed a jot. 
What I want to learn is the original core message of Buddhism before it was made into a religion. Where can I find texts for understand this message.
This is a matter of definitions. Nothing has changed. It always was a religion by a certain definition but not by other definitions. A good and well-known book is 'What the Buddha Taught'. 
There is no method for determining the truth and accuracy of texts except by using your own knowledge and judgement. It would be hopeless (and not good practice) to imagine that someone else can tell you which texts are 'the core message' and which are not. 
Some Buddhists argue that the Mahayana message is not 'core' some that it is. Only you can decide this matter. It would be more or less suicidal for a practitioner to trust other people to tell them which texts are important and which should be ignored except in very obvious cases. There would be no consensus on this forum as to which texts give the core message and which not or even what the core message is. This is as it should be, since we cannot read it in a book, or at least cannot be sure our interpretation of the book is correct. So as usual this is all about practice and the pursuit of knowledge that does not come from books. Armed with this we are then able to judge the books for ourselves.
For a start one would have to be able to judge the claim that Theravada is the correct doctrine and Mahayana is not. This is not a question that can be answered just by asking an expert but takes time and work. If you ask an expert you still won't know whether their answer is correct. 
Just thinking out loud and I'm not sure this is particularly helpful.     
EDIT: I'd recommend the Bhagavad Gita but that might be contentious. I'll mention my usual recommendation which is 'The Sun of Wisdom' by Kenpo Tsutrim Gymatso but this is rather more philosophical than practical. Or maybe 'Abhidhamma Studies' by Nyanaponika Thera. I read the suttas as Mahayana texts so could recommend them. A good book on Zen might be useful so perhaps 'Three Pillars of Zen' by Philip Kapleau or something similar.     

user43: Much of the original teaching, as remembered by students, is preserved in the Pali Canon. 
The texts are there, but how to understand and interpret them remains subject to debate. There's no concensus on what the core Buddha's teaching was. There are at least 3-4 (if not more) different interpretations.
One interpretation is called Theravada, and it focuses on obvious literal meaning of Pali Canon. Another is what I call the Buddhadasa interpretation (represented by Dhammadhatu here on this site), which understands the texts metaphorically as speaking about mind. The third is Madhyamaka, which goes even further into what they say Buddha really meant behind what he said. Then there's Zen and Dzogchen which took the main points from Madhyamaka and threw away Pali Canon. 
If you read some Pali Canon, you will see the first layer right away, what Theravada studies. If you try to connect it all together and understand how it all fits, you may rediscover some of the Buddhadasa's ideas on your own. Then if you are good at reading between the lines, you may notice that all of the Madhyamaka ideas come from the Pali Canon, too. Then, if you try to implement these ideas in practice, you will see that Zen and Dzogchen really know what they are doing. 
There's no concensus on how deep the teaching goes. It's up to you to decide, how much of the inferred meaning is too much, and how far you want to go.
That said, in every group of Buddhists there are always people who stick to their tradition superficially, thus turning it into a religion. If you can be free from sectarianism, you can learn from each school and assemble the entire puzzle by yourself. 

user8157: The original teachings are found in the Pali suttas, where the Refuge in the Dhamma (Teachings) is described as follows:

The teaching is well explained by the Buddha—visible in the here &
  now, immediately effective, inviting inspection, relevant, so that
  sensible people can know it for themselves.
SN 16.3

You start with the 1st three sermons of the Buddha, which are: 

Four Noble Truths and Noble Eightfold Path
Three Characteristics 
Three Defilements 

Then: 

Dependent Origination 
Emptiness

Also, where the Buddha declares what exactly he uniquely teaches: 

Handful of Leaves
"Suffering and the cessation of suffering"
Emptiness
Six elements; six bases for contact; eighteen mental examinations; and four noble truths

To understand the original teachings, the following words are best understood: 
(i) "jati" ("birth") or "jatiya", which means "self/social identity". 
(ii) "marana" ("death"), which means "death of identity". 
(iii) "kaya" (often translated as "body"), which means "group" or "collection" of aggregates.
(iv) "nirodha", which can mean "cessation" but often means the cessation of ignorance & craving.
(v) "beings" ("satta'), which on a spiritual level refers to thought created "idea" or "view".
(vi) "dukkha". in relation to the four noble truths, "dukkha" means "suffering" or "stress"; in relation to the Three Characteristics of the 2nd sermon, "dukkha" means "unsatisfactoriness", "ungratifying" or "unable to bring true happiness"; in relation to feeling, "dukkha" means "painful" or "unpleasant". 
Once the above is understood, you will be able to negotiate your way through the teachings. 
You can read these book to help you: 

Two Kinds of Language
Buddha-Dhamma for Students
The Shape of Suffering up to & including page 6
Nibbana For Everyone
Kamma in Buddhism


17322: <p>I happen to read this text from the <em>Buddhist Catechism</em> (which was written by Olcott, published 1881):</p>
<blockquote>
<p>Q. What striking contrasts are there between Buddhism and what may be properly called &quot;religions?&quot;</p>
<p>A. Among others, these: It teaches the highest goodness without a creating God; a continuity of life without adhering to the superstitious and selfish doctrine of an eternal, metaphysical soul-substance that goes out of the body; a happiness without an objective heaven; a method of salvation without a vicarious Savior; redemption by oneself as the Redeemer, and without rites, prayers, penances, priests or intercessory saints; and a summun bonum, i.e., Nirvâṇa, attainable in this life and in this world by leading a pure, unselfish life of wisdom and compassion to all beings.</p>
</blockquote>
<p>But any recent texts I read about Buddhism all make it appear as if Buddhism is no different from any other dogmatic religion. I understand that Buddhism also underwent a lot of changes due to local cultures and competition from other religions.</p>
<p>What I want to learn is the original core message of Buddhism before it was made into a religion. Where can I find texts for understand this message.</p>
 16489: <p>Below is the core of buddhism which extracted from <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.141.piya.html" rel="nofollow noreferrer">Saccabihanga sutta</a></p>

<blockquote>
  <p>"What is meant by not getting what one desires, that too is suffering?
  To beings subject to birth there comes desire: 'O might we not be
  subject to birth, and birth not come to us.' But this cannot be
  attained by mere desiring. So not getting what one desires, that too,
  is suffering. To beings subject to aging there comes the desire: 'O
  might we not be subject to aging, and aging not come to us...' (as
  before). To beings subject to disease there comes the desire: 'O might
  we not be subject to disease and disease not come to us...' To beings
  subject to death there comes the desire: 'O might we not be subject to
  death and death not come to us...' To beings subject to sorrow,
  lamentation, suffering, misery, and despair there comes the desire: 'O
  might we not be subject to sorrow, lamentation, suffering, misery, and
  despair, and sorrow, lamentation, suffering, misery, and despair not
  come to us.' But this cannot be attained by merely desiring. So not
  getting what one desires that too is suffering.</p>
</blockquote>

<p>But in above translation it is written with the word <code>too</code> (that <code>too1</code> is suffering). But in pali cannon there's nothing like that. It just say, <code>not getting what one desires (yampiccan na labhathi thampi dukkhan)</code>. The equal meaning to this in english would be <code>insatiable</code> <a href="https://www.google.com/search?q=define%20insatiable&amp;rlz=1C5CHFA_enLK860LK860&amp;oq=define%20insati&amp;aqs=chrome.0.35i39j69i57j35i39j0l3.3821j1j4&amp;sourceid=chrome&amp;ie=UTF-8" rel="nofollow noreferrer">meaning</a>.
This is the core of the real buddhism, once you understand then you will get a complete different picture about noble truths, dependent origination etc..
And one other correction should be, above explanation is given thinking <code>jathi</code> as birth of living beings, <code>jara</code> as aging of living beings. But that's not 100% correct, in <code>dhamma</code> what is highlighted as birth <code>jathi</code> is the birth of thoughts (good and bad both). And when you are in the right track you will get more wider picture on this. It's bit hard to explain here. If you are interested visit the <a href="https://puredhamma.net/key-hidden-dhamma-concepts/anicca-dukkha-anatta-2/anicca-inability-to-keep-what-we-like/?highlight=anicca" rel="nofollow noreferrer">this website</a>. </p>

<p>Due to the most of the misguided people this real dhamma is hidden. That's the nature of it. That's why it says <code>Buddha</code> is a very rear person who comes to the world only once for a long long time period. And exposed the reality (dhamma) of this world, which only buddha can be realised without help of anyone. So no need to worry about that.</p>

<p><strong>NOTE:</strong> Interesting question from someone who really wants / tries to understand the buddha's message. This answer might be down voted as it doesn't understand by the majority in this forum. Anyway I wrote it though I'm to be given down votes as it seems you are seeking the truth of the world.</p>
 14789: <blockquote>
  <p>a method of salvation without a vicarious Savior;</p>
</blockquote>

<p>this is not false, but people need a buddha to hear about the dhamma, which can be seen as a revelation, like when there is some prophet revealing some teaching to people.
For instance the people who keep saying that ''mediation is enough'' to be enlightened are competently wrong.
Even if people were skilled at whatever samadhi they cultivate,  they would fail be enlightened, since they did not hear about the dhamma and then investigate  for themselves the cause of the arising of dukkha and the cause of the cessation of dukkha.</p>

<p>Anyway, since there was always a vinaya and some bikkhus told by the buddha how to live and what rules to follow, it can be said that that the dhamma is a religion, at least for the bikkhus.</p>

<p>But since there is not what people crave the most, ie  cults, rituals, arts, entertainment, symbols, philosophy, as meritorious activities, even less for enlightenment, you can say that the dhamma is not religion, especially for lay people.</p>

<p>Currently people do not talk about pre-religion buddhism and post religious. They talk about pre-sectarian buddhism and post-sectarian buddhism, which is taken to mean before and after some council long time ago, eg after the 2nd council.
<a href="https://i.stack.imgur.com/XbUjR.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/XbUjR.jpg" alt="enter image description here"></a></p>

<p>For the oldest texts which are easily available in english, it would be as usual the texts in pali,  ie some texts from this long list</p>

<p><a href="https://i.stack.imgur.com/fKlFp.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fKlFp.png" alt="enter image description here"></a></p>

<p>and in more details here
<a href="https://en.wikipedia.org/wiki/Early_Buddhist_Texts" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Early_Buddhist_Texts</a>
<a href="https://en.wikipedia.org/wiki/Gandh%C4%81ran_Buddhist_texts" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Gandh%C4%81ran_Buddhist_texts</a>
<a href="https://en.wikipedia.org/wiki/Early_Buddhist_schools" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Early_Buddhist_schools</a></p>
 -1: <p>It seems to me the question is based on false premises. </p>

<p><em>But any recent texts I read about Buddhism all make it appear as if Buddhism is no different from any other dogmatic religion. I understand that Buddhism also underwent a lot of changes due to local cultures and competition from other religions.</em></p>

<p>I don't know what you've read but I have never found a text suggesting Buddhism is a dogmatic religion unless it was written by as sceptical person with no knowledge. </p>

<p>There have been changes and the teachings will continue to be represented, repackaged and re-explained to suit the times, but the message has not changed a jot. </p>

<p><em>What I want to learn is the original core message of Buddhism before it was made into a religion. Where can I find texts for understand this message.</em></p>

<p>This is a matter of definitions. Nothing has changed. It always was a religion by a certain definition but not by other definitions. A good and well-known book is 'What the Buddha Taught'. </p>

<p>There is no method for determining the truth and accuracy of texts except by using your own knowledge and judgement. It would be hopeless (and not good practice) to imagine that someone else can tell you which texts are 'the core message' and which are not. </p>

<p>Some Buddhists argue that the Mahayana message is not 'core' some that it is. Only you can decide this matter. It would be more or less suicidal for a practitioner to trust other people to tell them which texts are important and which should be ignored except in very obvious cases. There would be no consensus on this forum as to which texts give the core message and which not or even what the core message is. This is as it should be, since we cannot read it in a book, or at least cannot be sure our interpretation of the book is correct. So as usual this is all about practice and the pursuit of knowledge that does not come from books. Armed with this we are then able to judge the books for ourselves.</p>

<p>For a start one would have to be able to judge the claim that Theravada is the correct doctrine and Mahayana is not. This is not a question that can be answered just by asking an expert but takes time and work. If you ask an expert you still won't know whether their answer is correct. </p>

<p>Just thinking out loud and I'm not sure this is particularly helpful.     </p>

<p>EDIT: I'd recommend the Bhagavad Gita but that might be contentious. I'll mention my usual recommendation which is 'The Sun of Wisdom' by Kenpo Tsutrim Gymatso but this is rather more philosophical than practical. Or maybe 'Abhidhamma Studies' by Nyanaponika Thera. I read the suttas as Mahayana texts so could recommend them. A good book on Zen might be useful so perhaps 'Three Pillars of Zen' by Philip Kapleau or something similar.     </p>
 43: <p>Much of the original teaching, <em>as remembered by students</em>, is preserved in the <a href="https://suttacentral.net/" rel="nofollow noreferrer">Pali Canon</a>. </p>

<p>The texts are there, but how to understand and interpret them remains subject to debate. There's no concensus on what the core Buddha's teaching was. There are at least 3-4 (if not more) different interpretations.</p>

<p>One interpretation is called Theravada, and it focuses on obvious literal meaning of Pali Canon. Another is what I call the Buddhadasa interpretation (represented by Dhammadhatu here on this site), which understands the texts metaphorically as speaking about mind. The third is Madhyamaka, which goes even further into what they say Buddha really meant behind what he said. Then there's Zen and Dzogchen which took the main points from Madhyamaka and threw away Pali Canon. </p>

<p>If you read some Pali Canon, you will see the first layer right away, what Theravada studies. If you try to connect it all together and understand how it all fits, you may rediscover some of the Buddhadasa's ideas on your own. Then if you are good at reading between the lines, you may notice that all of the Madhyamaka ideas come from the Pali Canon, too. Then, if you try to implement these ideas in practice, you will see that Zen and Dzogchen really know what they are doing. </p>

<p>There's no concensus on how deep the teaching goes. It's up to you to decide, how much of the inferred meaning is too much, and how far you want to go.</p>

<p>That said, in every group of Buddhists there are always people who stick to their tradition superficially, thus turning it into a religion. If you can be free from sectarianism, you can learn from each school and assemble the entire puzzle by yourself. </p>
 8157: <p>The original teachings are found in the Pali suttas, where the Refuge in the Dhamma (Teachings) is described as follows:</p>

<blockquote>
  <p><strong>The teaching is well explained by the Buddha—visible in the here &amp;
  now, immediately effective, inviting inspection, relevant, so that
  sensible people can know it for themselves.</strong></p>
  
  <p>SN 16.3</p>
</blockquote>

<p>You start with the 1st three sermons of the Buddha, which are: </p>

<ol>
<li><p><a href="https://suttacentral.net/sn56.11/en/bodhi" rel="nofollow noreferrer">Four Noble Truths</a> and <a href="https://www.accesstoinsight.org/tipitaka/sn/sn45/sn45.008.than.html" rel="nofollow noreferrer">Noble Eightfold Path</a></p></li>
<li><p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.059.mend.html" rel="nofollow noreferrer">Three Characteristics</a> </p></li>
<li><p><a href="https://suttacentral.net/sn35.28/en/bodhi" rel="nofollow noreferrer">Three Defilements</a> </p></li>
</ol>

<p>Then: </p>

<ol start="4">
<li><p><a href="https://dhammadhatu.wordpress.com/2018/11/08/sn-12-2-paticcasamuppada-vibha%e1%b9%85ga-sutta/" rel="nofollow noreferrer">Dependent Origination</a> </p></li>
<li><p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn35/sn35.085.than.html" rel="nofollow noreferrer">Emptiness</a></p></li>
</ol>

<p>Also, where the Buddha declares what exactly he uniquely teaches: </p>

<ol start="6">
<li><p><a href="https://suttacentral.net/sn56.31/en/bodhi" rel="nofollow noreferrer">Handful of Leaves</a></p></li>
<li><p>"<a href="https://suttacentral.net/mn22/en/bodhi" rel="nofollow noreferrer">Suffering and the cessation of suffering</a>"</p></li>
<li><p><a href="https://www.accesstoinsight.org/tipitaka/sn/sn20/sn20.007.than.html" rel="nofollow noreferrer">Emptiness</a></p></li>
<li><p><a href="https://suttacentral.net/an3.61/en/bodhi" rel="nofollow noreferrer">Six elements; six bases for contact; eighteen mental examinations; and four noble truths</a></p></li>
</ol>

<p>To understand the original teachings, the following words are best understood: </p>

<p>(i) "<a href="https://en.wikipedia.org/wiki/J%C4%81ti" rel="nofollow noreferrer">jati</a>" ("birth") or "<a href="https://suttacentral.net/define/j%C4%81tiya" rel="nofollow noreferrer">jatiya</a>", which means "self/social identity". </p>

<p>(ii) "marana" ("death"), which means "death of identity". </p>

<p>(iii) "kaya" (often translated as "body"), which means "group" or "collection" of aggregates.</p>

<p>(iv) "nirodha", which can mean "cessation" but often means the cessation of ignorance &amp; craving.</p>

<p>(v) "beings" ("satta'), which on a spiritual level refers to thought created "idea" or "view".</p>

<p>(vi) "dukkha". in relation to the four noble truths, "dukkha" means "suffering" or "stress"; in relation to the Three Characteristics of the 2nd sermon, "dukkha" means "unsatisfactoriness", "ungratifying" or "unable to bring true happiness"; in relation to feeling, "dukkha" means "painful" or "unpleasant". </p>

<p>Once the above is understood, you will be able to negotiate your way through the teachings. </p>

<p>You can read these book to help you: </p>

<ul>
<li><p><a href="https://www.dhammatalks.net/Books5/Bhikkhu_Buddhadasa_Two_Kinds_of_Language.htm" rel="nofollow noreferrer">Two Kinds of Language</a></p></li>
<li><p><a href="http://www.buddhanet.net/pdf_file/bd_students.pdf" rel="nofollow noreferrer">Buddha-Dhamma for Students</a></p></li>
<li><p><a href="https://www.accesstoinsight.org/lib/authors/thanissaro/shapeofsuffering.pdf" rel="nofollow noreferrer">The Shape of Suffering</a> up to &amp; including page 6</p></li>
<li><p><a href="http://www.dhammatalks.net/Articles/Bhikkhu_Buddhadasa_NIBBANA_FOR_EVERYONE.htm" rel="nofollow noreferrer">Nibbana For Everyone</a></p></li>
<li><p><a href="https://www.suanmokkh.org/system/books/files/000/000/089/original/Kamma_in_buddhism_Buddhadasa_bhikkhu.pdf?1485253529" rel="nofollow noreferrer">Kamma in Buddhism</a></p></li>
</ul>
