Yes.
And also
* they're as rigid in their orthodoxy as any conservatives. As though they've taken the RW gripe about political correctness and made it real.
* They're as antiscience as conservatives, just different science. The basis of gender is biology, not attitude; a cross-gender cosplayer is still male or female. They'll tell you that GID is not a disorder; just ask someone who has it how well that works.