I do not know, and have not encountered, either JKR or those who have aggressed against her.
I guess the closest I have come is in a discussion with an old friend of mine - a former olympic athlete and member of the LGBT community. She, and many of her fellow athletes, have been vocally dismissive and dismayed by the (in her words)
appropriation of the word 'woman' as a mark of identity amongst the trans community.
My response wasn't brilliant - it did not inspire, nor did it help to accommodate, or to remove prejudice. Instead I was almost immediately deemed to be an outsider whose views are to be dismissed without question. In fairness to myself though, the single option I was given was "agree with us or be outcast".
But what was my view? It was simple: Words are not stable, and are subject, along with everything else, to the vagaries of time and fashion. Nobody owns them, and therefore nobody can appropriate them. If we choose to identify ourselves in terms of a word (the word: the map, not the territory) then we will inevitably be putting our identity at risk, because we do not (and cannot) determine future usage.
It is meaning: the territory, not the map, that matters. None of this is even new.
For example, l recall my grandmother (albeit back in the 1970's) asking "Do you know Colonel Smith, darling? He's a little bit queer, but he is so very gay".
Was she wrong or ignorant? Were the gay community at fault for appropriating these terms? Such queries are mere category errors: Mistaking the map for the territory. So if someone were to say "They aren't women!" and someone else were to say "Oh yes they are!", do we really have to pick a side? Words aren't even singularly defined: Many, if not all, words - and their meanings, depend upon the specific context in which they are used. This sort of dissent between such parties merely demonstrates that both parties are faulty of equivocation, and, at worst, using such equivocation to justify their outrage, anger, and intransigence.
So much for the word.
What about toilets, sports, and the rest?
We have two options - we either accept or reject that gender (or even sex) is binary. It has never been binary, of course, but that's never appeared to be an issue until far more recently: Beforehand, for toilets (etc), it was the unwritten assumption of systemic misogyny: If you are not a man, then you are a woman.
Does that still work? Lots of people hope so, because it creates an architectural nightmare to address toilets for any self-assigned gender. Pretty much the same for sex, once we accept the non-binary status. The proposition that a trans woman is a man is not any more sensible solution than any other binary categorisation.
So - where does that leave me? Is a trans-woman a woman? Sure, if that's what she wants to be, why not? Should she have the right to use a women's toilet, go to women's prisons, etc? I don't know : These institutions belong to an earlier binary culture. We could ask - should black women and white women share the same toilets?
What we *should do* is always going to be different to what we do. Personally, if we were living in a truly egalitarian environment, why distinguish at all? So on that basis, I guess, we must learn to accept, accommodate, and adjust- while recognising both the past, and our part in the present.
Sports - this is something which will self-regulate, based upon the sport involved. I have not much more to say on that.