Quietly dropping is not the same as someone being vocal and then retracing steps vocally.
Post US election the Labour party would actually have to be nuts to push some of the proposed trans related stuff though lolwithout robustly polling and better consideration - and by that they will understand robust polling isn't just about reaffirming the echo chamber because that's what's caught the Dems out.
It comes down to how good their strategists are and how vocal Tony Blair is privately/publicly (Blair gets it. However every time he opens his mouth in public he does the equivalent of making fairies die due to just how unpopular he is. He would be stupid to say much in public, but don't underestimate his private influence either).
And I do believe Starmer understands polling. He makes a point of playing the odds on that and avoiding controversial issues as a general rule.