A Republican who is also a Christian might be expected to support the first and the last two at least. Indeed, none of them should be partisan political issues--except, perhaps, the last.
Depends on the context with which those issues are being discussed and the proposed legislative solutions (and the very loosely related extraneous initiatives that get lumped in with it)
That's really what turns "shouldn't be political" issues into very political ones.
Typically, that's comes down to the proposals, and where they fall into the to the spectrum of "positive rights and negative rights" if folks are familiar with that concept (and that doesn't refer to positive/negative as in "good/bad")
Negative rights: Rights that oblige inaction and are not zero-sum game.
- ex: freedom of speech. there's not a "finite amount of speech" therefore me having that right doesn't diminish that right for anyone else.
- the right to be protected against unreasonable search: me having that right wouldn't require them to perform more unreasonable searches against you
Positive rights: Rights that oblige actions of others or require someone else to give something up, and can be a zero-sum game.
- ex: "there should be a right to healthcare" would require other people to chip in and a government to administer it
When a problem/issue is discussed, when the proposal falls in realm of positive rights, then it becomes a political issue.
So, to use examples you highlighted, racial justice.
Laws aimed at prohibiting police discrimination, ending qualified immunity for cops would examples of negative rights that have been proposed in the name of solving that.
Laws aimed at trying to do things like establish reparations, or establish a hiring quota are positive rights, in that they are requiring someone else to give something up in order for another person to get something.
on the LGBTQ+ issues.
Laws preventing discrimination against couples seeking marriage licenses would be negative rights, as there's no finite cap on marriage licenses, and a gay couple getting married isn't preventing anyone else from getting married.
However, the locker room one would be an interesting case that would definitely highlight the zero-sum game nature of positive rights.
Jane, a transwoman says she has a right to use the women's locker room, because she wants the right to have a locker room environment that makes her comfortable.
Sally, a ciswoman, says she's uncomfortable with that, because she wants the right to have a locker room environment that she feels comfortable in.
No matter which way you slice it, one person's
right to comfort is going to happen at the expense of the other person's. Hence the reason it gets political, as both parties naturally will be looking to pull whichever levers are available to them to prioritize their competing interests.