I think there are some nuances to be had here. I'm also concerned about the retention of female safe spaces, and as such agree with some of what JKR said. That said, my fear is of abusive men using GRA legislation to access those spaces, not of trans women. I think that given we are all at most risk from men, it makes sense to share spaces and share the fight against patriarchy, but I also think that part of collaboration should be recognising where each others' needs diverge as well as intersect. One of these divergence is that cis women need single sex spaces for a bunch of reasons, whether that's based in religion or in the fact that penises can be traumatic for women who've been sexually assaulted. There's no reason why we shouldn't fight together for both a shared space for trans women who need it and cis women cwho are happy to share, and a single sex space for cis women who need it. I can't see how it's transphobic to ask for this to be respected.
I also used to be very angry re: 'people who menstruate' but accept that people see this as person-centred and had good intentions with it. I just also think they overlook the fact that cis women have been reduced to their reproductive functions as the root of their oppression and that for this reason it's offensive to many. I see no reason not to make the language more inclusive, but in a way that respects this - just name everyone, ie cis women, trans men and non-binary people.
As regards BLM and social media, I see your point and agree there was definitely a lot of virtue signalling going on. However, I also think that much like the Me Too movement, the idea was to demonstrate that a critical mass of people - and especially white people - supported the movement in order to encourage others to start interrogating their own racism. White people's silence on racism is a huge issue for people of colour and BLM is in great part about changing that.
I empathise with her on the political front and I think it probably underpins a lot of the disagreements above. The last election in particular was hugely divisive, and if you are of the left it can be very difficult to see how you could switch from Labour to Tory at all, but especially to a Johnson-led government. If you believe first and foremost in an equitable society then that will include dismantling structural racism and support for the LGBT community. Johnson has been explicitly racist and homophobic on several occasions. I can understand that for her these issues aren't just differences of opinion, but differences in morality that she can't get past.
All that said, I think doing all this from behind a keyboard is what is driving a lot of divisions in society. I don't subscribe to the school of not having heated discussions with close friends - my friendship group differ on a lot of things and quite enjoy hashing them out over wine, and that's exactly how you actually come to see other points of view and maybe change your own. If she were of one of the minorities mentioned, I would understand it, but the point of allyship is to bring these topics into communities - like white straight cis ones - where they need discussing. Not to shout at you and cut you off and share private messages so you both end up entrenched in your positions!