Ah, okay. If we're going to have that discussion I guess I need to say where I am with this. I'm going to try and do this as simply and as straightforwardly as I can.
Everyone should be allowed to express themselves without fear of consequence as long as that mode of expression does not cause, contribute, or pose risk of harm to any other person peacefully living their own life. The trouble is that Trans Rights, as a movement, seems to be in direct conflict with Women's Rights.
I accept that choosing to live a life where you do not conform to expected gender roles does not come without risks, and that this obviously needs to be resolved. (My formative years were spent in a mining community in the 70s and 80s FFS! If I exhibited any behaviours that weren't considered typical for boys or men at the time - and I did, often - then it was usually trouble. This is why I had to learn to fight.) However, when these harms are discussed and examples cited, it appears to largely follow behaviours of male-pattern violence. It also appears to be that the go-to solution is for men to be allowed to access female spaces in whatever capacity as long as certain (possibly arbitrary?) conditions are met. Essentially, the solution for solving overwhelmingly male behaviours and attitudes to violence can only be solved by women giving up rights to single-sex spaces. I do not think that addressing underlying issues around male behaviours and how men are socialised will be resolved in any real way by asking women to accommodate men further.
My understanding of Rowling's stance appears to be that women should not be expected to give up any of the things which have been hard won over the course of decades because some men feel like they are more 'womanly' than 'manly'. She is not calling for people to be othered or demonised because how they choose to live does not confirm to restrictive gender roles but there are people who are prepared to attribute things to her based on extrapolations or her stated position because that position does not accommodate the potentially unchecked access of men to women's 'spaces' based on someone being in 'girl mode' for whatever period. Where she is being slandered, libelled or her privacy is otherwise impinged upon she is taking steps to protect that. You can argue whether the steps she takes legally are disproportionate or not, but she has the right and means to protect herself in whatever way she feels fit. As she's a billionaire, the legal means available to her are going to far outstrip those available to most of us and it might not be 'fair' to the general population that she can afford to keep very expensive legal teams on retainer for just this sort of thing. Ask yourself, though: if your name, reputation, right to privacy, etc. was being tested daily would you feel that you'd want to fight fair? (I learned to fight, What I learned was that there is no such thing as a fair one. In my experience, this is true regardless of how or where a fight happens.)
So. Do I feel that men should have access to spaces that - until very recently - were regarded as for women only? No. Do I feel that there is room for negotiation on this issue? No, not really. That implies that women have too many rights and protections and, historically, I think we can say that this has never been the case. Should women advocate for their own rights and protections? Absolutely. Should trans people advocate for their own rights and protections? Yes. Should women's rights and protections make way for trans activism? No. Should men learn to grow the fuck up and accept men expressing themselves in a feminine way in 'male spaces'? Yeah, I think so.
TL;DR - Not buying the Hogwart's game because it doesn't interest me in the slightest. If it did, JK Rowling being 'problematic' would not stop me.