Genderism is socially conservative. Why wouldn't the Tories be happy with heterosexual, class privileged, white males running the show?
I agree that genderism is conservative in its underlying philosophy, but it's currently not marketed that way. And many socially conservative men want to protect (some) women from wronguns.
Donald Trump has seen transgenderism as an opportunity to enhance his brand at no cost, what stops any of the Tories from doing the same?
Sadly I feel like Labour is too far gone. The woke misogyny has spiralled out of control and it's not even tempered by any right-wing protective instincts.