But bring over Gotham as a whole and everything important about it? there's a lot more nuance there.

If the supervillians are real as well, most likely there's going to be a supervillian that Republicans really love (I guess the Penguin?). Their opinion on Batman would hover around being neutral, perhaps slightly in favor until Batman beats the shit out of their favorite supervillian. After that, they'll accuse Batman of having "gone woke" and turn on him.