Everyone fighting for their rights who isn’t a cishet dude deals with some degree of this. Where do you think the idea that feminism is more than wanting equality came from? To be clear, it’s a bigger risk to trans people right now because more people think it’s ok to unalive you all on sight, but this is an old and widespread tactic in defense of cisheteropatriarchy.
The left doesn’t have the money to prop up a decent counterpropaganda apparatus.