It bugged me at first how they portrayed religion, lumping all Christians together into this extreme version that you see on the show. It's hard for me to imagine normal Christians going along with such a radical version of it.
But to your point, I think the fascist government they portray can happen with whatever ideology is taken to the extreme - with things you can't say or do, who can have what occupations, where you can go, etc. Cancel culture is a good example of that, like you said.