It’s probably not really about trans people for Rowling, or for some of the other stars on the other side (Margoyles is possibly one of the exceptions).  There’s a big split in the British left, between the 1990s establishment and intelligentsia, which includes Rowling (IIRC she was a Kennedy-era Lib Dem supporter before switching to Milliband’s Labour), and the more radical factions which lost control in the 1960s and were excluded from the Labour Party in the 1990s but which tried to regain control after Corbyn was elected leader. Really the argument is between neoliberals and “melts” whose rhetoric is much more left-wing than their voting record on one side and leftists on the other, but because attacking a party figure for being too far right economically  is likely to lead to suspension by the right-controlled Compliance Unit for some reason the question of whether MTF trans people are really women has become a proxy fight. I think it is re-fighting an argument from 2016 or so about who should hold a minor but media friendly position, But I’ve no idea why that particular topic was chosen. Non-labour people got involved because once the argument made it into the media a bunch of editors started paying their friends a few grand a piece (or more) for an article about how X was not a real feminist, and now it appears to just be a 4AM Twitter argument because a bunch of overpaid idiots won’t let anyone else get the last word.  Watson is interesting, because she’s built her feminist icon brand by joining the New Statesman/Guardian 1990s faction, but has managed to avoid getting involved in this argument. (I assume she, or someone close to her, has a functioning brain and has realised she doesn’t need the money and can’t win by getting involved.)