The very concept of a "rationalist" is an egregious one! What is a rationalist, really? The motte: "one who studies the methods of rationality, systematic methods of thought that result in true beliefs and goal achievement". The bailey: "a member of the social ingroup of Eliezer Yudkowsky and Scott Alexander fans, and their friends."

I've been Rationalist-adjacent for over 10 years now by my ideals, but have never taken part in the community (until this post, hello!) precisely because I find this fallacy throughout a lot of Rationalist discourse and it has put me off.

The motte: "Here is some verifiable data that suggests my hypothesis. It is incomplete, and I may be wrong. I am but a humble thinker, calling out into the darkness, looking for a few pinpricks of truth's light."

The bailey: "The limitations in my data and argument are small enough that I can confidently make a complex conclusion at the end, to some confidence interval. Prove my studies wrong if you disagree. If you respond to my argument with any kind of detectable emotion I will take this as a sign of your own irrationality and personal failings."

In my reading the bailey tends to come out in a few similar Rationalist argument styles. What they all have in common is that some lip service is usually paid to the limitations of the argument, but the poster still goes on as if their overall argument is probable and valid, instead of a fundamentally unsupported post-hoc rationalization built on sand. I tend to see:

1. The poster makes an arbitrary decision to evaluate the core hypothesis by proxying it onto a set of related, but fundamentally different, metrics from the actual thesis, where the proxy metrics are easily testable and the actual thesis is very broad. The evaluation that follows using the chosen metrics is reasonable, but the initial choice to even use those metrics as a proxy for the thesis question is subjective, unjustified, and the conclusion would have gone another way had different and arguably just as justifiable proxy metrics been chosen instead. The  proxy is never mentioned. Or if it is, it's is hand-waved away as "of course there are other ways to evaluate this question..."  But assuming that your toy metrics equate to a wider narrative is a fundamental error. Analysis is limited to the scope of what it's analyzing to stay accurate. 
2. The poster shows their work with some math (usually probabilities) to prove a real-world point, but the math is done on a completely hypothetical thought experiment. Can't argue with math! The entire meat of this hinges on the completely unjustified implication that the real world is enough like the thought experiment that the probabilities from one are relevant to both. But the thought experiment came from the poster's mind, and its similarity to reality is backed up by nothing. There is no more inherent reason why probabilities derived from a hypothetical example would apply to reality than random numbers thrown into the comment box would be, but because there's some math work included it's taken as more accurate than the poster saying "I think the world is like X" outright.
3. Using Bayesian reasoning and confidence intervals to construct a multi-point argument of mostly-unproven assertions that all rely on each other, so that the whole is much weaker than the sum of its parts. The argument is made as if the chance of error at each successive step is additive rather than compounding, and as if the X% confidence interval the author assigns at each unproven assertion is the actual real probability of it being true. But in reality, confidence intervals are a post-hoc label we give to our own subjective feelings when evaluating a statement that we believe but haven't proven. The second you label an unsupported statement with one of these you've acknowledged that you've left what you're sure of as objective reality. Each successive one in an argument makes the problem worse, because the error compounds. It would be more honest and objective for the argument to stop at the very first doubtful point and leave it there with a CI for future discussion. But instead I see a lot of "of course, this can't be really known right now, but I think it's 65% likely given the inconclusive data I have so far, and if we assume that it's true for the sake of argument..." and then it continues further into the weeds for another few thousand words.  

Obviously this comment is critical, but I do mean this with good humor and I hope it is taken as such. The pursuit of truth is an ideal I hold important.

(An aside: the characterization of post-modern argument in the OP is only accurate in the most extreme and easily parodied of post-modernist thinkers. Most post-modernists would argue that social constructs are subjective narratives told on top of an objective world, and that many more things are socially constructed than most people believe. That the hypothetical about the sun is used as an example of bad post-modernist thought, instead of any of the actual arguments post-modernists make in real life, is a bit of a tip-off that it's not engaging with a steel man.)

I think there's a tendency to assume the rationalist community has all the answers (e.g. The Correct Contrarian Cluster), which seems (a) wrong to me on the object-level, but also (b) at odds with a lot of other rationalist ideas.

If you point this out, you might hear someone say they're "only an aspiring rationalist", or "that's in the sequences", or "rationalists already believe that". Which can seem like a Motte and Bailey, if it doesn't actually dent their self-confidence at all.

Bayes!

The Bailey is that Bayes is just maths, and you therefore can't disagree with it.

When it is in inevitably pointed out that self described Bayesians don't use explicit maths that much, then they fall back to the Motte .. Bayes is actually just a bunch of heuristics for probabilistic reasoning.

I think there's a common Motte and Bailey with religion

Motte: Christianity and other religions in general are almost certainly untrue. Adherents to religions have killed many people worldwide. The modern world would be better if more religious followers learned rationality and became atheists.

Bailey: The development and continued existence of religion has on the whole been a massive net negative for humanity and we would be better off if the religions never existed and people were always atheists.

I don't even think the bailey is outright stated that often by smart rationalist as much as it is sometimes implied and only stated outright by zealous, less-smart atheists. The zealous atheists are likely succumbing to the affect heuristic and automatically refute the assertion that religion may have been a net positive historically even if it is no longer worthwhile. But they most often defend the claim that religion was terrible for humanity by citing to the Motte.

I feel like both sides of the "White Fragility" debate have some of this going on.

I don't feel like I've exactly seen rationalists on these sides (in large part because the discussion generally hasn't been very prominent), but I've seen lots of related people on both sides, and I expect rationalists to have similar beliefs to those people. (Myself included) 

https://www.lesswrong.com/posts/pqa7s3m9CZ98FgmGT/i-read-white-fragility-so-you-don-t-have-to-but-maybe-you?commentId=wEuAmC2kYWsCg4Qsr