There isn't actually such a thing as "rationalism". This is a label applied from outside to those who are trying to apply the concepts of rationality, or those who try to get into rationality but don't actually understand it.
Yes, there are schisms. No, there is not dogma. There are arguments people don't want to rehash, and there are fundamental axioms of reasoning.
The entire point of the exercise is to establish that certain things are true, and that this is not because of faith, and that disbelieving them cannot make them false.
>This is a label applied from outside
I don't think this is accurate. Most rationalists seem to self-describe as rationalists, and talk about rationalism as a "thing".
There is some dogma, sort of, in the form of The Sequences. (An extraordinarily goofy name that belies some of the mysticism-adjacent LARP that sought to treat the ideas as revolutionary. I suspect a 20 year old was behind it.) I say "sort of" dogma because people are aware that the studies referenced in there turned out not to replicate and have generally abandoned them. But you still see some references to them and vague reverence of them.
We probably understand this word very differently, because as far as I'm concerned, rationality (rational behavior) is essentially an exercise in behaving optimally, one that is thus strictly relative to some particular context. It is not just "facts and logic", and it is most certainly not universal, since universal optimality doesn't exist: https://en.wikipedia.org/wiki/No_free_lunch_theorem
> The entire point of the exercise is to establish that certain things are true, and that this is not because of faith
Taken at face value, that'd mean bridging the analog hole (https://en.wikipedia.org/wiki/Analog_hole), which is fundamentally impossible. Logic proves consistency, not truth, despite the many related terminologies suggesting otherwise. This is further skipping over how people segment the world different, even relative to themselves over time, which thus forms a coordination problem.
It reminds me to how HTTP is stateless. Yeah, it's stateless - all the state keeping has simply been laundered a layer above. It may sound tantalizing to position certain arguments as simply rational (i.e. correct/optimal), but all that ultimately does is sidestep the actual coordination part, which never really went away. There is still an underlying segmentation model being asserted, it is just now coated in self-righteousness, an illusion of rigor, drawing up a false dichotomy of "either you segment the world like we do, and then you're correct, or you're incorrect, and your segmentation is too".
See this rhetorical landmine in action in a sibling thread: https://news.ycombinator.com/item?id=48986530
Even if I go out of my way and interpret the word such that it merely means "acting on reason" (as opposed to some sort of nonreason), that doesn't mean much for the same reasons. You can have any arbitrary reason to act or think any particular way; possessing an explainable rationale on its own, even if internally coherent, is not necessarily one way or another.
You do realize you sound exactly like a cult member right? Like that's precisely how a scientologist would explain auditing to people outside the cult. Like this is "not dogma" just "fundamental axioms" that "is not because of faith, and that disbelieving them cannot make them false".
> The entire point of the exercise is to establish that certain things are true
And any domain where you can do that is not the real world. The real world is messy and you can't prove things the way you can in nice, tidy, theoretical domains like math. And the kind of logic where you have fundamental axioms of reasoning and you can prove theorems is just a subset of math. In the real world, things don't exactly satisfy the axioms, and boundaries are fuzzy, not sharp. Trying to pretend otherwise, while it might not strictly be "dogma" in the usual religious sense, is just as counterproductive.