They have a "trans rights" thing in their heads - and in their heads it's exactly the same as the fight for gay rights. Therefore - they support trans rights, because they're good lefty blokes fighting for equality. (And the silly feminists are just being a bit silly and hysterical. But women are.)
Yes exactly and so well put. With my long experience of hanging out with lefty types, what really terrifies them is the possibility of being accused of being a bigot or failing to be right-on in some way and dying of shame. Therefore they must blindly support any perceived oppressed minority group, and the slot gay and trangender into this category as if they were the same, though there are huge and important differences.
This also explains why they find it much easier to condemn Rachel Dolezal, a woman identifying as black – because in this case she isn't the more oppressed "minority", black people are. In this case, lefties can see that it's pretty offensive to black people's experience, for someone to simply decide they are black and expect to be treated as such. That works better for them because it fits in with their desire not to be racist bigots.
Lefties don't want to be sexist either, but they don't think they are because they pay lip service to feminism – but women come bottom of the pile when the chips are down.
Despite my cynicism I actually still am left-wing myself, but I've noticed more and more of this type of inconsistent and hypocritical thinking over the years.