I think you’ve got the key concept there: sharia. Ban adherance to or promotion of sharia, and you make it clear that it’s a political system, not a “worship” system, which we rightly see as incompatible with legal entry into, or residence in, the United States.
This is the insoluble contradiction. Leftists like exposing "contradictions" so make sure this one is exposed. Muslims, particularly the political ones like CAIR will claim Sharia is "religion" and claim 1st Amendment protections. At the same time, any true Islamic preacher will declare Sharia supreme and above any national Constitution.
I believe this is how to frame the debate regarding a serious restriction of Muslim immigration.