I'm thrown by being more in agreement with Theresa May than the leader of the Labour Party. Only on this one thing as far as I know, but still!

I think more people would be likely to engage in debate over Trans Rights than you think, to be honest. Exactly because we have more important and pressing things we are struggling with. People like an 'escapist' option, something which doesn't affect them but can take them away from their own miseries. That old saying 'misery loves company' is apt here. Especially when 'celebrities' lile JKR start weighing in with their 'opinions'.
It sounds awful, but it's true. To people who could never even imagine the realities of a transgender person's struggle for affirmation through identity, the whole situation is all to often an entertainment.
Throw in the amounts of toxic masculinity AND femininity swimming through 'working class' communities, still, and I'm sure I don't need to tell you how much resistance there is to any challenge to 'traditional' gender assignation.

The whole situation with the Labour Party is depressing quite frankly.