Conservative voters simply don't care enough. Whether that's because they don't understand, or they have limited exposure to the trans people they're supposed to hate

I think that's part of it. Trans people are such a minority you can go your whole life without knowingly meeting one if you don't live on a major metro area. What they hate is a bunch of caricatures they see on online social media, but there isn't much place to direct that hate. As opposed to the segregationist south, they had black people in your zip code they could easily walk up to and express their bigotry towards. It was easier to keep the hate flowing cuz there was actually a concrete "other" that was moving into your space. Some CHUD in Nebraska would probably have to drive two hours to find the nearest trans person. Not that they wouldn't but it takes some time to coordinate that shit,