I believe there's a school of thought that suggests that some children and teenagers who believe themselves to be trans may actually be gay or just gender non-conforming, and that some gay and particularly some lesbian people are themselves uncomfortable with the militancy of some trans activists.
https://news.trust.org/item/20190412100802-6md1q/
I don't believe I've read anything from Rowling that would fit my definition of hatred. Here's the most in depth she has been about her interest in the issue
https://www.jkrowling.com/opinions/j...gender-issues/
And I assume she signed the letter, not so much in response to the criticism she has received but in response to the woman she supported who was fired for saying "men can't change into women" (or similar). I've read about this from the perspective of trans people, gay people and feminists who feel uncomfortable with the focus on gender rather than biology and on transwomen accessing or working in previously women-only spaces such as women's refuge centres. And after reading a fair amount from all sides of the issue I still don't quite know what to think. This suggests to me that it's a complex issue and it's foolish to pretend it isn't. In fact pretending it isn't seems the definition of what the letter calls a "tendency to dissolve complex policy issues into blinding moral certainty". (As to Rowling having received nothing more severe than criticism, well, she has received hundreds of death threats I believe)
But I didn't really want to focus on this.
Aaron, maybe I'm just a dupe of the right wing media, who knows. I would happily read any stories about right wing suppression of speech (genuinely) because this isn't about partisan politics for me. I'm sure there will be many examples around the Israel/Palestine issue that you suggest is Chomsky's reason for signing the letter.
When I was in my teens I was a massive fan of The Dead Kennedys, the left wing, San Francisco shock-punk band. I read as much about them as I could, which wasn't easy pre-internet. I learned, through magazines and liner notes, that their lyrics and artwork had often been the target of censorship and even an obscenity case, which they fought and which financially ruined them. Their attackers were evangelical Christian groups, the "Moral Majority" (the name of one of their songs) and well-meaning 'concerned liberals' like Tipper Gore who created the "Parental Advisory" labels that started being stuck on records in the 80s. I knew nothing about US politics, sitting in my bedroom in northern England, other than Ronald Reagan was an idiot and used to be in bad westerns. But I knew whose side I was on. The moral majority is just wearing a different hat these days, but very often when I read about this stuff (in my right-wing news sources of choice, the guardian and the BBC

) I get exactly the same feeling. I know it when I see it.
Edit: I assume you'd agree that Germaine Greer, whether you think she's just a transphobe or not, is a genuine feminist.