"The four points of the compass be logic, knowledge, wisdom and the unknown. Some do bow in that final direction. Others advance upon it. To bow before the one is to lose sight of the three. I may submit to the unknown, but never to the unknowable." - Roger Zelazny, in Lord of Light
"To the rational mind, nothing is inexplicable; only unexplained." - The Doctor
"One man's 'magic' is another man's 'engineering'. 'Supernatural' is a null word." - Robert Heinlein
"To surrender to ignorance and call it God has always been premature, and it remains premature today." -Isaac Asimov
"When you believe in things that you don't understand, then you suffer; superstition ain't the way..." - Stevie Wonder
Some people like to conflate the idea of an overarching philosophy that people use to frame and understand the world - a worldview - with a religion. "Maybe you're not a Christian or Muslim or even a Buddhist or Confuscian," they'll say, "but that just means you've made a god out of secularism or democracy or yourself or material wealth or..."
But a worldview is not the same thing as a religion, though worldviews often have religious components. So far as I've seen, there's a single, very simple difference between a religious and a non-religious worldview. Religious worldviews include some concept of the supernatural, and non-religious ones don't.
The best definition I've seen is in the quotes at the top of this page. The 'supernatural' is 'incomprehensible' - unknowable by humans - something forever beyond human ken, something we will never be capable of understanding. Different terms are used - the 'ineffable', the 'mystery', and so forth - but the basic idea is the same.
Think about the difference between the notion of the 'powerful alien' (a staple of science fiction) and the notion of a 'god' in a religion. What's the essential difference between them? In the stories, they both do amazing, astonishing things. But a powerful alien is (ultimately, eventually) comprehensible - often in the story humans are able to figure out some way of duplicating its powers, or interfering with them, etc. Gods, though, are beyond what humans can do, and there's no point in trying to figure out why or how they do what they do.
Now, it may be that there are things out there that are 'unknowable' by humans. Perhaps they're 'too big for us', too complex for us to comprehend. Or perhaps they are too alien, and simply won't fit within the mental categories, the 'toolbox' humans have available. It's certainly possible, and can't be ruled out a priori. But this point is, at best, of only philosophical interest. It doesn't have any practical bearing at all.
Epistemologically, the 'unknowable' is a troublesome concept. How can we, in practice, distinguish between something 'currently unknown but comprehensible' and something 'forever unknowable'? (We could also add other categories like 'knowable in principle but impractical to discover' and 'knowable and practical but, just by bad luck, will never have the explanation stumbled upon'.) From a practical perspective, the only way to tell which category something falls into is to try to understand it; if you succeed, then it was knowable. The problem is, if you fail, you can't conclude that it's unknowable. It might be... but it also might be the case that you just didn't happen to figure out something knowable, and you or someone else might have better luck on a subsequent attempt.
Think about all the things that have been confidently declared to be supernatural that have turned out to be perfectly explainable and comprehensible. (I've listed a few here.) Early in human history, practically everything was considered to be the direct result of supernatural forces, but over time more and more things have moved to the 'explainable' column. (BTW, it's worth pointing out that so far as I can see, nothing has ever moved the other way, from the 'explainable' to the 'supernatural' column...)
People once thought that no 'mechanism' could ever be made to play chess. The game was thought to be too subtle, too complex, to require too much 'intelligence' for a 'machine' to play it. This was an article of faith for Edgar Allen Poe when he wrote his famous essay on Maelzel's Chess Player: "It is quite certain that the operations of the Automaton are regulated by mind, and by nothing else. Indeed this matter is susceptible of a mathematical demonstration, a priori. The only question then is of the manner in which human agency is brought to bear." But now we have Deep Blue, and yet no one thinks that Deep Blue is actually a mind. It's a truism in the Artificial Intelligence field that "A.I. is whatever we can't do yet." It's an article of faith that human intelligence, human self-awareness, is fundamentally unknowable. Once a part of that is explained, well, it's no longer considered part of the 'mystery of what it is to be human'.
If you decide that something is fundamentally incomprehensible, you will stop trying to understand it. Richard Feynman once joked that "You don't understand Quantum Mechanics, you just get used to it," but he never stopped trying to advance understanding of QM, despite how counterintuitive it is. And it's worth noting that QM is not quite as incomprehensible as it's popularly portrayed - if it were, the computer you're reading this on could never have been designed and built.
As I've shown above, the notion of the "unknowable" has serious practical issues. But the assertion that God is "beyond human comprehension" also has grave theological implications that people avoid addressing. If you really want to assert that God is totally beyond human conception, that means you can't be sure of anything about it - anything at all.
Dividing by zero is undefined in mathematics. It just doesn't work. If you assume that you can divide by zero, then mathematics itself breaks down, and you can prove literally anything. For example:
Something's wonky there, no?
Asserting there's things you can't know is the intellectual equivalent of dividing by zero. Once you go there, all bets are off. You can 'prove' anything you like.
What if there is some kind of God (or gods), and It's exactly like a shepherd... down to the shearing and slaughter, too? (I'm sure sheep feel comforted by the presence of the shepherd... until the knife comes down.) If a God is totally beyond anything we can understand, there's no way to disprove this. By definition, It's perfectly capable of fooling us perfectly. There's no way to tell.
I brought this up with one theist, asking him how he knew that God wasn't just fooling him that He was good. He replied, "Impossible, given Christ's suffering." But that's exactly the point - you can imagine a sheep thinking, "I know my shepherd is good and would never hurt me! He even fought that wolf off that one time!" Then, one day, the shepherd wants to have a feast...
If you try to claim that you have evidence that a God is trustworthy and benevolent, then you are by that very fact denying that such a God is incomprehensible. Evidence only applies to comprehensible things. If you say something's incomprehensible, you're unavoidably saying that no amount of evidence can prove anything about it. You don't get to pick and choose. If the evidence for unnecessary suffering and evil means nothing, then the evidence for good that theists want to claim also means nothing.
It is entirely possible to accept that there are things that are unknown, while still not accepting the notion of things that are unknowable (in the sense discussed above). There are lots of things we don't know - indeed, it's pretty certain that "the number of things we don't know" is greater than "the number of things that we do know". (It's very likely the case that "the number of things we know" is much less than "the number of things we don't even know that we don't know about".)
We know of some limits to our knowledge today. General Relativity and Quantum Mechanics are beautiful scientific theories, and their predictions have each been confirmed to many decimal places. However, in certain areas, they make radically different predictions. At least one and probably both are wrong to some degree. Unfortunately, we can't test them right now because we don't have any black holes handy. But, eventually, we may well be able to get a probe to a black hole and check it out. In principle the tests could be performed.
Accepting that there are things that we don't know is not the same as accepting that there are things that we cannot, even in principle, know. As discussed above, the notion of 'the unknowable' adds nothing from a practical perspective. There is no way we can tell the difference between 'something we can never understand' and 'something we can eventually understand but do not understand yet.' We've seen plenty of cases where giving up on ever understanding something turned out to be unjustified.
Now, there are many things we won't ever know, for various reasons. There are probably many species that died out in the past without leaving fossils that survived to the present. We'll never know about them unless we develop time travel someday. But no one would call those species 'supernatural'.
It's quite true that unknowable entities can't be ruled out a priori. Maybe there really are some out there. But... how would you prove it? If we encountered a real, honest-to-goodness 'miracle', what evidence could you possibly present that it was caused by a god and not a powerful alien? The most you could ever say would be, "A god hasn't been ruled out, yet." From a practical perspective, I can't see what the notion of 'supernatural' buys you. Unless you're trying to justify not even trying to understand something.
(I'm dubious that any actual miracles have been observed, but even if I were presented with one, I'd just get to work trying to understand it.)
With this in mind, it becomes clear that atheism is not a religion in the most critical sense of the term - it does not accept the notion of supernatural (and thus unknowable) beings or forces or influences. It's worth noting that the 'religions' that least depend on such notions - e.g. Buddhism or Confucianism - are also the most likely to be called 'philosophies' or something similar. There's already doubt that they 'count' as religions.
Now, just because a worldview doesn't include the idea of the supernatural does not mean that it is automatically free of dogma. One definition of dogma is "a doctrine or code of beliefs accepted as authoritative"; another is "a point of view or tenet put forth as authoritative without adequate grounds". As has been made entirely clear in the past, non-religious philosophies and worldviews (including various flavors of atheism) can be just as dogmatic as any religion. For example, consider communism as practiced by Stalin and Mao.
Both of them made a dogma of Lysenkoism, and explicitly rejected neo-Darwinian evolution. Unfortunately for the people of the Soviet Union and China, however, reality failed to conform to "worker's science" and massive crop failures resulted in widespread famine. It's ironic that 'atheism' gets the blame for the millions of consequent deaths when it was a quasi-religious, dogmatic adherence to communist principles that was the primary cause.
A worldview that doesn't include supernatural elements can be just as rigid and dogmatic - or as flexible and open - as any religion. But so far as I can see, a willingness to accept propositions without evidence (as any belief about an 'unknowable' being must be) is a lot more likely to lead to tenets being accepted "without adequate grounds".
We can have "supernaturalistic" and "naturalistic" worldviews, as well as "dogmatic" and "flexible" worldviews, in all possible combinations. I try to be in the "flexible naturalistic" category. I have at least some common ground with the "flexible supernatural" and "dogmatic naturalistic" types, but I have some fundamental disagreements with them as well. And I've got very little in common, philosophically, with "dogmatic supernaturalists". (See, e.g., here or here.)