I believe it simply comes from them believing that these people are destroying their country. They see trans acceptance as proof they are losing the culture war which they feel will have political consequences for them. It isn't going to affect them but they have been told it will by every pundit and cultural convention they are familiar with. At best they see it as strange and the ground is moving from beneath them. To put it more simply, its fear. They don't understand it so their reaction is to hate and destroy it because it signals societal change.
Everything is zero-sum game to them. If someone is getting more recognition and rights, they believe it means they themselves have less.