There was a discussion about this in another forum I'm on. I didn't take part but I was interested to read how it is being perceived elsewhere (most members of the group are American).
They automatically assumed that she was being transphobic, and the thread was mainly about their disappointment in her. When pressed about exactly what, the views seemed to be that her books were all about being inclusive, but her tweets were the opposite (I don't think anyone had read her essay, and I suspect very few the tweets). They suggested that there was nothing wrong with the term 'people who menstruate', especially as the article it referred to was apparently specifically about menstruation, and thus it was a much more inclusive term as it included those who menstruated but didn't identify as women, and excluded those who were women but didn't menstruate. They seemed to think she was being particularly horrible by implying that those who didn't menstruate (or not any longer) weren't women (I know, logic isn't always their strong point). But it was very difficult to know what to say back in response to those sorts of assumptions. How to say that erasing the term 'women' still matters, even if the specific instance she referred to was about menstruation (I can't actually remember if this is true), and how to explain that she wasn't saying only people who menstruate are women. Or that nothing she said was about trans rights anyway. They assume that she wasn't inclusive because she wasn't including transmen or non-binary people, when actually it was the transwomen that were sending the death threats etc.
They're all very woke and well-intentioned and want to be inclusive, very much the sort of 'why are you afraid to pee next to a transwomen in the restroom?' sort of people, and without going into huge details about things that they won't likely believe anyway, it is so hard to say anything that doesn't immediately get you labelled bigot and non-inclusive.
I suspect a lot of people who are saying they don't want to sign something like this are similar to the people in that group. You can't really ask them what they find horrible, because to them, she IS being non-inclusive. I never know how to have this discussion.