I think there is a fundamental difference. I think that the Tories' initial support for self-ID came from a place of insecurity. They got Section 28 and gay marriage wrong and so were concerned not to get gender wrong and again be dubbed the nasty party. (It is important not to forget that in 2015 when Stonewall added the T, no one questioned Stonewall and its influence was everywhere.)
I suspect that none of the male MPs who talked knowledgeably and passionately about the safety of women and girls, ever really believed that a man could put on a dress and become a woman. Indeed I am pretty sure they didn't. However other than David TC Davies, who grasped early on that this was an important issue, they carried on busying themselves with affairs of state.
Over time the briefing and lobbying by so many, including the right wing media and groups like Conservatives for Women, has given them the confidence to trust their moral compass and speak out.
Quite why the equivalent, male, northern, Union backed, Labour feels unable to do the same is unclear. The climate and culture do not seem to exist, and they can see what happened to Rosie Duffield, so they will be ignoring it as a "woman's issue". (I suspect that several may already be struggling with ultra left-wing activists within their local parties, so don't want to give any additional reason for deselection.) David TC Davies had all manner of complaints and abuse thrown at him when he was the sole head above the parapet. Rosie has almost certainly had worse. They are our brave lightening rods. Lets hope that Labour MPs including JC join her in the same way that a few good Conservative MPs (Jackie Doyle-Price, Kemi and even Liz Truss did then joined by Miriam Cates and others) joined Davies, until the trickle became a stream.