One answer to a Quora question about JKRowling goes as follows:
It isn’t what she herself has said, although she’s been generally insulting and has displayed great ignorance by denying the fact that the Nazis destroyed scientific literature about trans people. The problem is that she has publicly supported TERFS who *have* said bad things – people who approve of the murder of trans people (I’ve seen one here on Quora blaming Brianna Ghey for her own murder), and who want to have armed male guards in women’s loos to shoot any trans woman who tries to be in the same space as cis women.
Part of Rowling’s problem boils down to her inability to count. Yes, a very small minority of trans women are bogus and/or predators (I used to know one: they do exist). A small minority of lesbians are also sexual predators, and some teenage girls will sexually attack other females as a form of bullying, and even rape them with implements. The risk of an individual trans woman being a predator probably is higher than the risk of an individual cis lesbian or straight teenage girl being one, but since the number of cis lesbians and straight teenage girls is *enormously* higher than the number of trans women, they’re where the threat lies, if you want to get worked up about already very small dangers.
By getting hysterically fixated about a statistically tiny risk, TERFS have set the cause of women’s liberation back 50 years, making it seriously dangerous for any cis girl to appear anything other than fluffy and girly, or for any old woman to grow a moustache.
With regard to the first paragraph (and ignoring the fact that although the Nazis destroyed lots of scientific literature, some of which may have related to trans people, it is not clear that they did so for that reason per se rather than out of fear of sexual ambiguity in general) I wanted to comment on the “guilt by association” argument that some of those she supports may have said bad things. One can support the ideas of the Model T and Volkswagen without endorsing the other ideas of their promoters. The sins of the latter are of course so well known that any sign of approval of anything he did is suspect, but it is still quite possible for someone to endorse Henry Ford as belonging to the pantheon of great industrialists without being assumed to share (or consciously overlook) his racial views. So I still wonder if it is clear that JKR has ever supported the approval of murder of trans people, or the idea of having “armed male guards in women’s loos to shoot any trans woman who tries to be in the same space as cis women”.
Actually, I suspect that public washrooms are a non-issue for most of those who are often identifed as TERFs, but that their concern is more with places where they might have to disrobe in the open, and in the case of people who have been sexually assaulted with penises with wanting to have some guarantee that the person counselling them does not have one.
And with regard to the last paragraph in that answer, I have been told that what many feminists object to is not the existence of trans women but the suggestion that any girl who appears anything other than fluffy and girly, or who does not feel the need to eliminate any sign of facial hair, must accept the “reality” that she is actually a trans man.