I'm going to be an apologist for conservatives for a sec, just for the sake of giving out my theory of mind of these people.
I think this all happens mostly due to the stress trans people are inadvertently causing their parents. When your kid comes out of the closet, this will happen to a parent regardless of how liberal-minded they are. Even if you have no problem with the concept, your kid being trans brings about new kinds of threat scenarios you never had to think about before. If you're a sensible, smart and handsome person like I truly fucking am, you can process it in a few years and come out as not being a 100% asshole towards the issue.
But if your reference group is republican church goers, there's a high probability that such a person just simply does not have the mental or social toolset to process it in any sensible way. They will construct a toxic viewpoint for this issue, strengthen it from outside sources and then start to spread that toxicity.