The rigidity is the problem, not the they/them, isn't it?
Of course it's entirely possible for people to go entirely off the rails, even to the point of being part of a suicide cult (body deformation cult seems possible given precedent from historical societies)--but rather than being reflexively worried, I'd wait to see evidence. I don't think the evidence is particularly strong.
We have a great deal of evidence that parents are, throughout the ages, worried about "kids these days", and usually if there is something wrong with "kids these days", it's totally not what the parents are worried about. (Biggest problem currently: irresiliency, brought on by parents being too worried.)
I agree that the side that used to be "liberal" is forgetting what that means, which leaves us a choice between two illiberal poles with a rapidly thinning middle, but I don't think the "they"ing is particularly correlated. If you're going to have some fad, emphasizing that we're all humans (sorry--we're speciesist here) seems better than needing to wear a particular type of shoes.