I'm going to take a guess here and say that the majority of evangelicals (which is the largest block of conservatives right now) do take issue with boob jobs. They also don't like it when girls cut their hair short or wear non-feminine clothing, to give other related examples. At least, that's the evangelicals here in Florida that I know.

There's varying degrees of just how much deviation from their cultural norms are allowed (I'd argue that's what defines how "conservative" they are). This is why conservatives can get extremely upset when LGBTQ+ people are allowed to be themselves in public... Because it normalizes them.

Conservatives know that if it becomes normal for their kids to see/meet gay dads/moms, trans people, or other non-binary people on a regular basis the very definition of what they believe to be "normal" will be swept right out from under them in the minds of their children. The very foundation of what they believe won't be passed on to the next generation.

That's why conservatives are obsessed with children "being exposed" to LGBTQ+ topics/people in school. They know that if their kid grows up around completely harmless LGBTQ+ people that their kid will just naturally start to believe that these people are harmless (because they are), normal, and "no big deal". That's their worst nightmare!

I'd go so far as to suggest that it is impossible (today) for someone to claim they're a conservative while simultaneously claiming that LGBTQ+ people are born that way. There's nothing conservative about that (it's beyond cognitive dissonance). Furthermore, it goes completely against the Bible's teachings that women are property! Property can't just up and change itself into a man/actual thinking person!