On reflection I think they way they responded to the question made them realise the Trans pledge and particularly them saying that WPUK and LGB Alliance were hates groups were a step too far.
So they agreed a strategy to deflect away from that saying the problem was about not having a civilised debate (nothing to do with us Your Honour calling people hate groups). Hypocrites.
And if that C4 presented wasn't such a total numpty he would have asked them to prove they were have groups.
We've had all this publicity about Tory cabinet advisors making off the wall remarks, but here we have 2 potential leaders of the Labour Party signing false statements. Who would trust a politician like that?
It says far more about the inner factions in the Labour Party than any concern for voters.
And I suspect that still for the vast majority of people (in or out of the Labour Party) they just dont think it is an important issue.
I will be very surprised if Kier Starmer doesn't win the vote because I think people will be looking at who the general public will vote for. And given existing prejudice against women, I think they will think he is a better prospect.
It wont even necessarily be about who is more or less a Corbynite.
According to some reports many ex members have rejoined to make sure a more middle of the road person gets elected, and of the 3 he is it.
I think the issue of trans rights vs. women's rights will just be viewed as a niche issue.