Many conservatives are full square for gay marriage these days, so there's a difference. You are talking about the religious community. And with that said, I don't think gay marriage should be outlawed. I don't think it's right, but I also don't think drinking or cheating on your spouse is right, and I don't argue for them to be illegalized. I think conversations are a lot more peaceful way to reach agreements than pushing for illegalization.
Idk what you mean by rejection of science, but i know many scientific-minded conservatives both irl and via the internet (both of my parents included in the irl section).
I was for the creation of the vaccine. I wouldn't be comfortable taking it if i knew a risk was involved (especially since i have a condition that makes vaccines less safe for me). But i don't think they should be illegalized, and i don't think people should be punished for not getting it.
No separation of church in state is again a religious desire and is not limited to the Republican party.
And in my opinion they should teach all kinds of ideas in schools and the arguments for and against them, and let the kids decide what they believe for themselves. That has always been my stance there. I don't think they should just teach atheism in schools, and i don't think they should teach a specific religion in schools. I have learned history from perspectives i haven't necessarily agreed with, and all i can safely say is that i have a wider understanding of differing Weltanshauungs, and the sad thing is many people cannot say the same today. School is supposed to be a place of information, not indoctrination.