Classical Less Wrong text about "what is rationality":
https://www.readthesequences.com/What-Do-I-Mean-By-Rationali...Shortly: believing what is true, and choosing the actions that lead to the things you value.
If the sky is blue and you can verify that by looking at the sky, it is reasonable to believe that sky is blue, and it is unreasonable to believe that the sky is green just because some authority or your favorite political party said so. If you know that eating poison would kill you, and if you want to live a long life, it is reasonable to avoid the poison, and unreasonable to eat the poison.
These are separate skills, because many people know what to do, and yet don't do that, or are good at following their beliefs, but the beliefs happen to be wrong. Studying the rational beliefs is called "epistemology", studying the rational actions is called "decision theory".
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The word "rationalism" is used by many people in different ways: https://en.wikipedia.org/wiki/Rationalism_(disambiguation)
In internet discussions inevitably someone mentions the 17th century definition of "rationalism" as opposed to "empiricism" as the only historically valid meaning of the word. But for example, the approach of Karl Popper is often called "critical rationalism", and although the Less Wrong philosophy is different from Popper's, it is closer to him than to the 17th century "rationalists".
(The difference between Popper and Less Wrong in a nutshell: Popper treats arguments in favor of a theory, and arguments against a theory, as two fundamentally different things that follow different rules. Less Wrong treats all arguments the same way, using the Bayes Theorem. In practice, the difference is smaller than it might seem, because Popper's main concern was to never treat a theory as a 100% truth, especially when there is evidence against it, and Less Wrong agrees that you should never treat any theory as 100% likely. The advantage of Less Wrong approach is that you can also apply it to probabilistic theories. For example, one person says that a coin is fair, another person says that actually the coin is 55% likely to come up heads, and 45% likely to come up tails. I have no idea how you would decide this problem from Popper's perspective, because any experimental result is kinda compatible with both theories, it's just the more coinflips you make, the less likely some of those theories become; but there is no clear line when you should call one of them "falsified".)
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I think this is the kind of thing where you simply can't make everyone happy, no matter what you do. As an analogy, imagine a world where every time you say e.g. "American president", at least three people in the thread remind you that actually Donald Trump is not a president of the entire continent, only of a part of the North America. So the next time you pay extra attention and say carefully "the president of the United States", and then everyone is like: "you mean the American president, why don't you speak simply?".
There is a community around Less Wrong. Whatever we call them, we should choose the name so that it is obvious that we refer to them, and not to the 17th century philosophers who believed that evidence is not necessary. Things are real, words are just labels.
At the beginning, it was just a few dozen people from different parts of the planet, reading the same blog. They referred to themselves as "aspiring rationalists". (As a label that applies to an individual who aspires to be more rational.) I would be okay to use this label, but apparently many people are too lazy to say "aspiring" all the time, and when you only say "rationalists", (1) it sounds smug, as if you believe that you already are perfectly rational, rather than you are trying to become more so, and (2) inevitably, some outsider will mention the 17th century philosophers. I think people used "Less Wrong community", "rationality community", "LessWrong-style rationalists", "x-rationalists", and maybe a few other words. But there was always pushback against using "rationalist" without any adjective.
As a long-time member of the community myself, I don't have a problem with anyone using any of these labels. I know what you mean, and I am not going to play dumb. It's the non-members who need to coordinate on a standard label for us, so that they are not confused about who they are talking about. And I am even okay with them choosing a label that we don't use. (I am doing the same to other groups, e.g. I say "Mormons" instead of "The Church of Jesus Christ of Latter-day Saints".) If the world decides to call us "rationalists", so be it... but then don't blame us for using the same label as the 17th century philosophers, because we don't. I think that "rationality community" or "Less Wrong community" are both nice options. (Just please don't call us TESCREAL because that's a crazy conspiracy theory.)