I think there is another reason SJWs (and others) may dislike “rationality” that is getting buried here:

1. The author is not a good reasoner, and while arguing over these experiences, often says stupid things, and gets told ze is irrational

There is a difference between an argument not being phrased in a reasonable way and the argument itself being stupid. When my husband and I were first married I would win must of the arguments NOT because I was necessarily right (as later came to realize) but because I was a better rhetorician. I could lay out my case in an orderly fashion. I could work commonly agreed statements into my arguments. I could anticipate counter arguments and set-up to counter them. I could model possible external circumstances and present those that supported my view. This lead to a situation where my husband constantly felt steam rolled. He might not be able to articulate logical fallacies but he could feel the effects of his preferences constantly being overruled by mine. I needed to learn to back off and respect his views even if they weren’t phrased as elegantly as mine. Even though I could use a rationality is winning approach to maneuver the situation so that “we spend all the entertainment money on sci-fi books and none on cable” looked like the “rational” decision, I eventually came to realize that, to serve my overarching goal of a flourishing marriage, our hedonic preferences needed to be weighted equally and split the money between our preferences “I really, really want X,” is never stupid or irrational in and of itself. It’s just a preference. To the extent that some SJWs seem to want to say “I really, really want X,” and leave their argument at that, then rationality is irrelevant to them.