If you look upthread you will see my light bulb moment. In summary
Men will do what suits men. They see women in a support role.
Men are often quite nervous about gay men. They want to be open and liberal and accepting. They don't fully trust their own instincts, so will look to the gay man, in a group, on the board, etc, to set the moral direction.
So gay man says trans is the same as gay and you need to be accepting, they go along with that.
If gay man says that this whole LGBT+++ thing has gone to far, that sex and gender are different and that all trans is doing is reinforcing old fashioned stereotypes. Then women's views will be heard.
As for the gay man, it might depend of his own experience. Did he face prejudice so is quick to believe transwomen have the same. Is he opportunistic like Stonewall and see trans being the new oppression that can prolong his EDI career. Or, like plenty of other men does he see things the way we do, but unlike us he is listened to.
Which is sort of leading me on to why gay man and ethnic minorities do well in the Conservative party. (And which needs a whole other thread.) Perhaps there is less of an imposed script, so they have more freedom to call things as they see them.
My gay Conservative colleague was invited by Stonewall to join a register for LGB Councillors, something he accepted. Now the gender stuff has kicked off he would not do the same again. He loses nothing by distancing himself. Not playing the Stonewall game would probably get a Labour Councillor in trouble.