What would pseudo-rationalism even be? Purported rationalism, yes, but the rationalism would be just a smokescreen for positions that are not rationally derived and therefore not addressable by means of rational argument.
I don't understand why you think asocialism or self-interest is the opposite of rationalism. I think that's on an orthogonal axis.
Bonus points for obfuscating your positions with in-group jargon and mathematical terminology that you don't actually understand. Nattering on about 'Bayesian priors' won't make you any more effective at reasoning than coconut headphones will help land airplanes, but it might keep people from challenging your ideas. If it does so because they've written you off as a fool or because you've successfully snowed them, you'll never know.
The fundamental question of philosophy: how do you tell a rationally derived belief from an irrationally derived belief?
The former, I could change, given enough data.
The latter, I am willing to die for (or rather, attack other people for). However, I could change it after hanging out with different people for long time.
So? The western states killed and enslaved just as many under various names (from christianity and manifest destiny, to democracy and free trade and "the free world").
What happened in the name of an idea doesn't mean the idea is bad or that what happened is an inevitable part of the idea.
Ayn Rand begins with axioms, and logically derives her position from there. (Well, maybe. I suspect that at least to some degree, she already had her position, and derived her axioms from there, then argued for her position from her axioms.) So I attack her position by saying that in her third axiom, she mis-defines consciousness, and the rest of her errors follow from her flawed starting position. That's rational. "It leaves me cold" is not a rational response. (It may be an indication that you feel there's something wrong with the position, even if you can't define it or prove it, and that's fine. But it's not a rational response.)
(Sorry if it comes across overly pedantic and twisted: non-native speaker, not enough sleep, words hard.)
There's no way to arrive "logically" at value judgements.
You can just use logic as a klutch to support your pre-determined positions (and, of course, which is totally rational as a practice, to spread, support and enforce them).
"Things are what they are. There is only one reality, namely the way things are."
That's only true for the least interesting things: objects and their arrangements in space-time.
On that, the huge majority (besides maybe crazy people) agrees anyway, when they see them, or when they're given evidence of them (e.g. a photo of a laptop on a desk. 99.999% of the people will agree there's a laptop on a desk there).
For anything else, politics, values, claims and the veracity of claims, morality, motives, aesthetics, goals, etc., there is no single way things are, there are ways people perceive them, and there are different interets, worldviews, and ways of interpreting them.
What is the "reality" or "non-reality" of "I'm willing to die for my country"? Or of "I find it OK to make money stealing"? Or "You should treat people well even if you are not forced to|?