On what basis do you say that?
Quite a few conservative MPs have said that they are aware. Including the (for the moment) PM.
They have said that they will not institute self-id.
They have initiated things like the Cass report which is the beginning of changing the whole approach to treatment of children.
They did not go ahead with including gender identity in their conversion therapy bill.
They have begun to look to roll back the damage done in schools.
They have begun to push back significantly on the involvement of SW in the civil service.
They have been clear that men in women's sports are not, in their view, ok.
Compared to the LP they are miles ahead the LP would not done any of this institutional stuff and in fact would be running merrily in the other direction. SW schemes would be the order of they day and they would still be setting the bar on policy, therapists would not be allowed to do anything besides affirm, there would be no Cass report, there would be self-id.
Look at the government of Canada if you want to see where we'd be if there had been a Labour government.