I want to say as well, this is one of the good things about having an unusually hands-off No10 operation.
Central control of Whitehall waxed and waned a bit under the Tories, and reached a peak under Chairman Dom, but generally any big policy had to go through the PM, so you needed the right person having the PM's ear.
I can imagine Boris Johnson having gone totally TRA if not for Nikki da Costa being in the right place at the right time. And I wonder about who persuaded Theresa that self-ID was a low-cost vote winner.
Starmer declared at the start that he wasn't going to do that, he was going to trust his cabinet. Which isn't always a good thing as we can see from studying Rachel Reeves' decisions.
But in the case of rolling back genderwoo, I'd speculate that Starmer being hands off has allowed Streeting, Phillipson and McFadden to stake out a rational position without getting bogged down negotiating with No10 and whoever happens to have Starmer's ear at the moment. Starmer himself is bringing up the rear, which makes sense considering how terrible he's been on the issue.