Can I just say, because it's come across my dash recently, that saying "not all republicans support laws like this" when it comes to anti-choice, anti-lgbtq legislation is technically true but functionally bullshit?
If you vote republican but you do not vote for people who vote for anti-choice legislation or anti-gay marriage legislation or you stop voting for people as soon as they push through this kind of legislation, then yes, you do not support it. But, in most states, I have no idea who you'd have left to vote for.
Let me make this crystal clear, no matter what you support philosophically, what you support with your vote (and with your contribution dollars) is what you support. It is not relevant that you aren't anti-choice or anti-gay marriage if you vote for politicians who support anti-choice or anti-gay marriage legislation. You don't get to claim to stand with people fighting this legislation, you don't get to claim to be on the right side of history, and you don't get to be offended when people "lump you in" with the anti-choice and/or anti-LGBTQ movement when you vote for the politicians who work to oppress women and LGBTQ people. And while I understand that everyone has competing priorities when they vote, saying "I'm not a one-issue voter" or "I vote conservatively because I'm a fiscal conservative" is the same as saying "your rights and your humanity are not my priority". That's what it means. (Unless you only vote when there is a fiscally conservative, pro-lgbt rights, pro-choice candidate.) So own your vote, you're the one who made it.
This is a representative democracy which means, I'll say it again, what you support with your vote IS WHAT YOU SUPPORT.