Oh, don't get me wrong, anyone involved with national-level republican politics is either a bigot, or cynically pandering to the bigots (which is worse imo).

That said, I think a lot of people fear/hate trans people because they really can't conceptualise what being trans actually means. Pointing out that if, as a 40-something man who has an embedded self-image of themselves, you find yourself going bald it's not uncommon or unnatural to feel a sense of sadness or loss or unhappiness because your internal and external self images no longer align. You can then point out that some people might choose varying methods - everything from subtle changes to how they style their hair to full on medical interventions - to try and regain some feeling of control over their external self image and bring it closer to their internal identity. There is a straight line from there back to gender affirming care for trans people, and that makes it a smaller jump for people to extend empathy into a situation that they find so foreign that "trans people are actually just all pedos and rapists something something men in women's changing rooms" is a more plausible explanation for them