Therein lies the problem for Labour in my opinion, who won't even define what a woman is.
As much as desperate Tories would love to make some kind of faux nationalist culture wars the battleground issues in 2024 (as having failed on every issue of substance that’s all that is left) the reality is that the vast, vast majority of voters will probably care a lot more about:
keeping a roof over their head
cost of food
decent pay
heating
the NHS
schools
… than they will about which MP said what and when in the trans debate, and which nutty speaker got their appearance cancelled at some university, and which 18th century figures’s statue was thrown into some river.