If a Muslim community refuses to issue liquor licenses, you’re going to see Christian Nationalists accuse the municipal government of “operating under Sharia Law” in order to justify a state-level take over of the administration.

Sure, you would see that. But they’d be wrong. Unless a muslim-majority community somehow changes the constitution to allow them to create laws on religious grounds. But it seems more likely the people to do that would be the evangelicals.

Of course republicans are gonna cry “sharia law” every time a muslim person participates in politics. That doesn’t make it accurate.

If you’re implementing policies in defiance of the state’s majority party

I’ma stop you right there. In this political system, minority parties don’t implement policy in defiance of the majority. Practically speaking, that just doesn’t happen, because it takes a majority vote to pass, and it has to pass two chambers of congress. And unless it passes with supermajority, it needs the executive’s signature. And even then it has to stand up to scrutiny by the (albeit corrupt) supreme court.

All that applies even at the state level, although some states have a different name for their highest court. But the process is the same.