David lammy is correct. At least he’s logically correct/consistent from the point of view of socially liberal politics.
The socially liberal centre left (not to be confused with the communist far left which isn’t liberal) generally believes in individual rights and freedoms and in ‘liberating’ the individual from the constraints of customs, traditions, biology, economic circumstances or anything else constraining individual freedom.
When the wishes of one group conflict with the wishes of another they tend to stand up for the smaller less powerful group.
Those people stood up for women wanting to advance in a male dominated society in the 1980’s. They stood up for gay people against social Conservatives in the 2000’s. Of course they’re going to stand up for trans people against feminists in the 2020’s. It’s exactly the same principles they are following that the liberal left have always had. Only thing is many people here won’t see that. Nevertheless I’m sure they will continue to vote Labour/liberal left regardless :)
It’s not an accident that all major centre left/liberal parties embrace trans rights with the exceptions being so few they almost prove the rule. They will also eventually end up suppressing speech that offends by taking the side of someone’s ‘right’ not to be offended over another’s ‘right’ to speak their mind. It’s baked into the ideology and will get there eventually.