Difference between Buddhist and materialist views of no self?

There is no such thing as "doctrine of materialism" in the Pali suttas. Therefore, this term "materialism" should be completely ignored.

The Buddha taught all things, including Nibbana, were "elements" (MN 115) and this is a supreme enlightened view in Buddhism.

However, there are some alien doctrines the Buddha criticized that included the doctrine of elements because these these alien doctrines also included the doctrine of the inefficacy of kamma and the non-benefit of giving. These doctrines did not believe in morality, virtue & kammic inheritence, which is why the Buddha criticised them.

As for the doctrine "annihilationism" ("ucchedavāda"), in the Pali, this does not refer to disbelief in kammic inheritence & disbelief in causality (which are called "natthikavādo", "akiriyavādo" and "ahetukavādo"; per MN 60) or the disbelief in life after death. The term "annihilationism" ("ucchedavāda") refers to the view that a "self" ("atta") ends at "death". "Annihilationism" ("ucchedavāda") is a "self-view", which is why it is wrong view. Please refer to DN 1.

Annihilationism (Ucchedavāda)

There are, bhikkhus, some recluses and brahmins who are annihilationists and who on seven grounds proclaim the annihilation, destruction and extermination of an existent being. And owing to what, with reference to what, do these honorable recluses and brahmins proclaim their views?

Herein, bhikkhus, a certain recluse or a brahmin asserts the following doctrine and view: 'The self, good sir, has material form; it is composed of the four primary elements and originates from father and mother. Since this self, good sir, is annihilated and destroyed with the breakup of the body and does not exist after death, at this point the self is completely annihilated.' In this way some proclaim the annihilation, destruction, and extermination of an existent being.

DN 1

Please respect the Pali suttas, study Dhamma in the right way and take refuge in the Buddha rather than take refuge in teachers and worldly scholars that teach contrary to the Buddha.

Apart from what you have mentioned, materialists usually think that the mind is a byproduct of the brain. In other words, electrical traces stored in neurons. This is not the case in Buddhism. Brain is a concept according to Buddhism. The reality is fundamentally grouped into 2 categories: the mental(Nama) and the physical(Rupa).

The four noble truths hold true at all times regardless of what one believes. But one is not able to attain enlightenment, if one holds to the view that all mental activities end at death. This belief is called Saggawarana & Maggawarana: conceals the path to heavens and conceals the path to enlightenment.

Here's a related answer by ven.Yuttadhammo.

This question has many facets, but I will answer in as straightforward a manner as I'm capable. You ask:

Still, I want to ask here and verify that this quote is accurate, and not a misunderstanding. i.e. is a belief in rebirth and karma what distinguishes the Buddhist from the materiast[sic] view on no self?

I'm not sure your paraphrase of the meaning of this quote is accurate insofar as it seems to imply that a belief in rebirth and karma is the only distinguishing factor between a materialist view and what the Buddha taught. If that paraphrase of the meaning is accurate, then the answer is a decided No! to my mind. There are many differences including the truth of rebirth between what materialists think and what the Buddha taught. Still, we should be careful to distinguish between different views that can be lumped together under the designation "materialist" yet may have subtle differences. For instance, there is the ancient Indian materialist school of Charvaka or Lokāyata which although seemingly has many similarities with modern materialists or scientific reductionists, may have material differences. Yes, the pun was intended :)

Anyway, did the Buddha distinguish his views from the ancient Indian materialists? Yes! And he did so in the Pali canon as well as in Mahayana Sutras. For instance, in the Samaññaphala Sutta: The Fruits of the Contemplative Life this account is given of an encounter with the ancient Indian materialist Ajita Kesakambalin who was a contemporary of Buddha Shakyamuni:

"Another time I approached Ajita Kesakambalin and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings and courtesies, I sat to one side. As I was sitting there I asked him: 'Venerable Ajita, there are these common craftsmen... They live off the fruits of their crafts, visible in the here and now... Is it possible, venerable sir, to point out a similar fruit of the contemplative life, visible in the here and now?'

"When this was said, Ajita Kesakambalin said to me, 'Great king, there is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly and practicing rightly, proclaim this world and the next after having directly known and realized it for themselves. A person is a composite of four primary elements. At death, the earth (in the body) returns to and merges with the (external) earth-substance. The fire returns to and merges with the external fire-substance. The liquid returns to and merges with the external liquid-substance. The wind returns to and merges with the external wind-substance. The sense-faculties scatter into space. Four men, with the bier as the fifth, carry the corpse. Its eulogies are sounded only as far as the charnel ground. The bones turn pigeon-colored. The offerings end in ashes. Generosity is taught by idiots. The words of those who speak of existence after death are false, empty chatter. With the break-up of the body, the wise and the foolish alike are annihilated, destroyed. They do not exist after death.'

So on the narrow question of whether the Buddha distinguished his teaching from that of the ancient Indian materialists I think there can be no doubt so long as one accepts the validity and authenticity of this Sutra. Of course, one could quibble with the definition of "materialist" and say that this is an incorrect designation, but for the purposes of your question I think the definition is fine, right? Moreover, contemporary researchers of this school of ancient Indian thought give it this label. Please let me know if you disagree.

To go further, I think the view described above and attributed to the ancient Indian ascetic Ajita Kesakambalin is in fine concordance with many modern day scientific reductionists although they would surely replace the four elements with modern day conceptions of matter and energy. Also, "Generosity is taught by idiots" is also in concordance with many immoral or amoral scientific reductionists. At best, modern scientific reductionism is neutral on the question of ethics.

If so, then do the Buddhist teachings on no self and the Third Noble Truth only hold if one believes in rebirth, in the literal sense?

Not sure what you mean by "only hold", but I think you are asking something like, "besides moral questions and knowledge of the truth of rebirth, what other differences can be found between modern scientific reductionists and the teachings of the Buddha?"

Many! However, here I'll only list one that is very pertinent and profound to my mind: the Buddha taught that matter and energy are unreal and not inherently existent. We should regard this phenomenal world filled with matter and energy as like:

“As a star, a visual aberration, a lamp, an illusion, dew, a bubble, a dream, lightning, and a cloud – view all the compounded like that.”

This is decidedly not the program of the modern scientific reductionist or scientific realist which believes wholeheartedly in the objective solid physical world made of matter and energy and governed by the fundamental laws of physics. And yet, the Buddha taught that all is ephemeral like a dream without even the slightest bit of inherent or fundamental existence. Hopefully, you can see how the two views are in conflict :)

A different question, but one which I think you are pointing at is whether belief in karma, rebirth and the moral/contemplative life is necessary to achieve the soteriological goals of Buddhism. For my part, I do believe it is at least highly highly highly advantageous. I'll even go so far as to say I'm not sure how one could achieve the soteriological goals of Buddhism without belief in karma, rebirth and the moral contemplative life.

To my mind, refuting the truth of rebirth requires something akin to the materialist trap: it hypostatizes or reifies matter and energy as fundamental and explains consciousness as emerging from it. This is akin to saying that the phenomenal world is intrinsically or inherently existent; but it is utterly not. How can one dispute that consciousness continues even after the breakup of the body without reifying the body and regarding it as fundamental and inherently existent in contradistinction to consciousness? I don't think it is possible.

Nevertheless, I'm convinced it is absolutely necessary to regard karma, rebirth, and the moral life as similarly ephemeral and lacking of intrinsic existence as all other phenomena including consciousness, matter and energy, in order to achieve the final soteriological goals of Buddhism.

If Buddhist and materialist schools share the same view on the most obvious meaning of anatta (quoted above), then what distinguishes the Buddhist view from the materialist view on no self?

Well, here we get into perhaps the subtle differences between "materialist" schools. I can't speak to the ancient Indian Charvaka materials school, but it is most obvious that modern scientific reductionists of the atheistic persuasion do not believe in any kind of permanent, unitary or independent self. So it is clear that someone like say Daniel Dennett (a modern day materialist) shares the belief in the most coarse meaning of anatta with Buddhists even though he does not - to my knowledge - identify himself as Buddhist; he does not take refuge in the Three Jewels and he does not share our soteriological goals nor even believe they are possible to accomplish. This is not to say that our soteriological goals themselves distinguish between the coarse and subtle meanings of emptiness! Just that if you believe it is possible to accomplish our soteriological goals, then it is manifestly evident that a meagerly coarse understanding of anatta cannot by itself accomplish them. Which brings us to...

Is there a not-so-obvious meaning of anatta which materialist/scientific reductionist schools fail to understand?

Yes!

And I believe understanding it is imperative to achieving the soteriological goals of Buddhism. Now, that isn't to say that understanding the most coarse meaning of anatta is useless. This is emphatically not the case! In fact, understanding the most coarse meaning of anatta is necessary waypoint to understanding the more subtle meanings. This is, after all, why the Buddha taught it :)

So how can one go beyond the coarse understanding to the more subtle meaning? Well, this is the question isn't it...

At this point, I want to make clear that I probably know nothing or that anything I might know is merely regurgitated (poorly) from much more qualified teachers. I'm just a lowly suffering sentient being trying to find liberation and aspiring to the motivation to achieve this for the benefit of all. In other words, take everything I say with a grain of salt and go check for yourself :)

Anyway, Je Tsongkhapa in his Great Treatise on the Stages of the Path (Volume 3, pages 204 - 215) spells out the actual object to be negated. Understanding the actual object to be negated is a key prerequisite to reasoning out the subtle meaning of emptiness and distinguishing it from the coarse meaning. This is very difficult and requires a ton of merit. Why? Because we have been blinded to this object - just assuming it a priori - since beginningless time. It is so ingrained in our thinking and taken as a given that we are just blind to it. This is our ignorance and delusion.

For lack of better terms we call this object many things: intrinsic existence, inherent existence, true existence, essential existence etc., But terms can't help us too much unless we know what they are referring to and for that we have to develop our intuition through study. To overcome our ignorance we must develop certain knowledge that nothing whatsoever has the type of existence pointed at by those inadequate terms.

If I had to pick one section of Je Tsongkhapa's Treatise that tries to directly answer the question of what the object of negation is it would be this section on page 212 and 213:

Question: How does ignorance superimpose intrinsic nature?

Reply: In general, there appear in Candrakırti’s texts many usages of verbal conventions such as “nature” or “essence” with regard to objects that exist only conventionally. However, here in the case of reification by ignorance, there is, with regard to objects, be they persons or other phenomena, a conception that those phenomena have ontological status—a way of existing—in and of themselves, without being posited through the force of an awareness. The referent object that is thus apprehended by that ignorant conception, the independent ontological status of those phenomena, is identified as a hypothetical “self” or “intrinsic nature.” For, Aryadeva’s Four Hundred Stanzas says:

All of this is without its own power; Therefore there is no self.

Commenting on this, Candrakirti’s Commentary on the “Four Hundred Stanzas” says:

It is that which exists essentially, intrinsically, autonomously, and without depending on another....

Thus, he says that those are synonyms. “Without depending on another” does not mean not depending on causes and conditions. Instead, “other” refers to a subject, i.e., a conventional conscious- ness, and something is said not to depend on another due to not being posited through the force of that conventional consciousness. Therefore, “autonomously” refers to the nature of an object that has its own unique ontological status or manner of being. It is just this that is called “essence” or “intrinsic nature.” Take, for example, the case of an imaginary snake that is mistakenly ascribed to a rope. If we leave aside how it is ascribed from the perspective that ap- prehends a snake and try to analyze what the snake is like in terms of its own nature, since a snake is simply not present in that object, its features cannot be analyzed. It is similar with regard to these phenomena. Suppose that we leave aside analysis of how they ap- pear—i.e., how they appear to a conventional awareness—and analyze the objects themselves, asking, “What is the manner of being of these phenomena?” We find they are not established in any way. Ignorance does not apprehend phenomena in this way; it apprehends each phenomenon as having a manner of being such that it can be understood in and of itself, without being posited through the force of a conventional consciousness. Candrakırti’s Commentary on the “Four Hundred Stanzas” says:

Without any doubt, what exists only through the presence of conceptual thought, and does not exist without conceptual thought, definitely does not exist essentially—as in the case of a snake that is imputed to a coiled rope.

Thus Candrakırti states how phenomena do not essentially exist.

Therefore, what exists objectively in terms of its own essence without being posited through the power of a subjective mind is called “self” or “intrinsic nature.” The absence of this quality in the person is called the selflessness of the person; its absence in phenomena such as eyes, ears, and so forth is called the selflessness of objects. Hence, one may implicitly understand that the conceptions of that intrinsic nature as present in persons and objects are the conceptions of the two selves. It is as Candrakırti’s Commentary on the “Four Hundred Stanzas” says:

“Self” is an essence of things that does not depend on others; it is an intrinsic nature. The nonexistence of that is selflessness. Because of the division into objects and persons, it is understood as twofold: a “selflessness of objects” and a “selflessness of persons.”

Now, let's say someone truly arrives at this subtle understanding... how does this help to achieve our soteriological goals? The best way I can answer that is this allegory that is given in Insight into Emptiness page 258:

“For example, a young woman may want to have a child. When she is asleep, she dreams she gives birth to a child and is elated. But later in the dream, the child dies and she is devastated. However, on waking, she sees that neither the exhilarating appearance of having a child that brought her joy nor the horrible appearance of the child’s death that caused her anguish is real.”

Understanding upon awakening that the dream was unreal the young woman was able to dispel the exhilaration as well as the devastation she felt. Likewise, upon truly realizing that all this phenomenal world is unreal - utterly not existing as it appears - we too can "wake up" and achieve our aims by cutting off the craving and attachment we acquire by believing in this completely ephemeral and hallucinatory "real" world.