I can see why it would concern you, especially since you think all Republicans believe that. Fortunately for all of us, all Republicans don't think that way. As I've said many times, I have several problems with the GOP, and one of the main ones is they want to be the morality (broad use of the term) police.
The difference between you and I is that you think every Republican thinks that way, whether or not that actually express it. You think they are just waiting to act on it the moment they can.
You speak of reproductive rights in a really strange way. You apparently believe that a woman should be able to abort a baby right up until the baby is born. You are entitled to that belief, but it's a perfectly legitimate belief that a viable fetus deserves protection of it's life.
I'm not sure what protections you are demanding for LGBT people. I'd like to get a more specific complaint on that. As far as I know, no adult is being refused treatments or surgeries if they want to change gender.