Absolutely. But the question isn't how ordinary people would perceive it; it was how Rowling intended it. Rowling's goal was to say that trans women are not women. She used a dogwhistle instead of saying that directly. But what other purpose could she have been trying to accomplish there?
She explained her purpose in a longer blog post (https://www.jkrowling.com/opinions/j-k-rowling-writes-about-...). She thinks (and I tend to agree) that phrases like "people who menstruate" are terribly degrading, and emphasizes at length that "trans rights are human rights".
She does also have some concerns about trans women in women-only spaces, but depending on which polls you read, either a slim majority or large plurality of people agree with her concerns.
I have read that article. She argues obliquely that trans women are not women[1], and she suggests that trans women are often dangerous predators[2]. Her statement that "trans rights are human rights" is an intentional dismissal of that opinion as a form of virtue signaling[3]. She may believe that some trans women are women, but in general she believes that there is a "material difference" between trans women and women.
As for the term "people who menstruate," I could see how that could be true. I could also see a term that's designed to specify a subset of women (pre-menopausal cis women who menstruate) as well as a subset of trans men. It is not being used as a general replacement for "women"; it is specifying the relevant people more precisely than the word "women" would. Isn't that specificity and accuracy what we want to see?
[1] "I know transition will be a solution for some gender dysphoric people, although I’m also aware through extensive research that studies have consistently shown that between 60-90% of gender dysphoric teens will grow out of their dysphoria."
[2] ", I do not want to make natal girls and women less safe. When you throw open the doors of bathrooms and changing rooms to any man who believes or feels he’s a woman – and, as I’ve said, gender confirmation certificates may now be granted without any need for surgery or hormones – then you open the door to any and all men who wish to come inside."
[3] "It would be so much easier to tweet the approved hashtags – because of course trans rights are human rights and of course trans lives matter – scoop up the woke cookies and bask in a virtue-signalling afterglow."
I think your assessment of her opinions is correct, but again, I think this is something that most people believe. It's widely acknowledged that it's rude to go up to a trans woman and say "hey you are not a woman", but the idea that there's no material difference between trans women and cis women is not widely accepted.
> I think this is something that most people believe
I think it's about 50/50. The one good, recent poll I found on the issue seems to suggest that (I mentioned it at more length in the other subthread here). So I definitely don't think that there's an overwhelming consensus, but I do think that it's a pretty standard opinion.
As for the "material difference" thing, sure. I think almost everyone would agree with that. My problem is that I believe Rowling is using it as a dogwhistle to argue that (most) trans women are not meaningfully women.
