Don't get me wrong. I took statistics in college, and we covered Bayesian methods. They can't be controversial because Bayes' Theorem is a theorem, meaning it's proven. But the attempt to apply its terminology to lengthy but "soft" arguments seems like pure clutter.
Nevermind that the first principles lose all context of the original issue - we're in a world of pure logic, where we can use theorems! To the rationalist community, everything looks like a good opportunity to write a lengthy essay reinventing the wheel with Bayes theorem. It's a cargo cult of basic statistics dressing up otherwise uninteresting arguments.
It's very tedious for people like myself who actually studied statistics and apply it professionally. Bayes theorem is barely even a theorem - it's literally a basic rearrangement of the axioms of probability. It's not some supreme revelation that imbues arguments with more credibility. Most of the time I see it invoked in discussion, it's not even rigorously quantified. You can choose arbitrary priors, so at the end of the day you never arrive at an objective truth. It's profundity for its own sake, and nothing is really achieved.
It is also certainly true that garbage in and garbage out, i.e. if you feed garbage inputs, you'll get garbage out (Bayesian or not), but the advantage in my opinion of having a framework for making decisions in cases of uncertainties is extremely useful. It is often hard to really apply this for ordinary life situations, (and maybe often not worth it), but even then it's useful to think about priors/evidence, even if you don't particularly care about the final number.
With the very important proviso that the events you're uncertain about are at least probabilistically quantifiable and the "priors" are credible. It's very easy to write a long winded essay arriving at any conclusion you want if it's a subject with significant uncertainty and you can make a halfway decent appeal to whatever priors you want.
The second is there's no way to set priors for silly ideas and they won't admit some things just ain't gonna happen, which means they've accidentally started a religion by refusing to not believe in various logic traps they call "existential risks" like Roko's basilisk, evil AI gods enslaving them, and so on.
* for some reason they call themselves rationalist which implies being "rational", aka "always right", even though they are explicitly not rationalist, but empiricist!
Being able to think about probabilities is useful, if they're quantifiable. And conditional probability plays a useful role in that process.