I do see that Proudofitbabe and I am sympathetic to a lot of your post but he does have to appeal to young voters who are more susceptible to GRA arguments.
This however is the big miscalculation any of the parties dabbling in self id have made (including the Tories under May).
They've assumed this policy is an overall net vote winner. It's not.
If the LP dropped self id, the younger left wing voters are not going to start voting blue.
You may lose a few votes to the Lib Dem's, but so what? In the grand scheme of being in govt that's irrelevant.
By supporting self id on the other hand you will lose swathes of support, especially from women but also from people who just think the whole thing is nuts and are not going to vote for a party whose representatives look increasingly bonkers and out of touch when interviewed by referring to a male rapist as "she".
I still think what happened in Scotland has not really fully sunk in.
The SNP and NS had levels of support the LP can only dream of from a quite diverse political base that united around the issue of independence.
The fact that gender reform was a significant issue in her downfall speaks volumes about the toxicity of this as a policy for most voters.
KS's problem in renouncing self id isn't because it's the right thing to do to or to win more votes, it's that he's dealing with a party of MP's, grassroots membership and trade unions who are all captured by this ideology and he can't afford to piss them off or he might not be leader for much longer.
That's why I can't trust the LP. Whatever KS says, he's just one person and behind him are legions of people putting pressure on him to implement self id because as a party it's consumed by an arrogance that it's their job to educate the electorate rather than represent them.
By contrast the Tory membership cares about one thing. Winning. So a u-turn on self id was a no brainer when they finally cottoned on they'd lose more votes than they would gain over this issue.
The LP need to realise that if they want to be in power they need to stop dictating/educating the electorate and start from a position of listening to them.