Unfortunately, the only law recognized in Islam is Muslim law, the Sharia. The 'proper sphere' for Islam includes politics; I've not read of any disagreement on this among muslims.
If a religion does not recognize the same 'proper sphere' as you do, then what? How do you propose to convince the mullahs that they are outside their proper sphere? I doubt that even you and I agree on what the proper sphere for religion is, except that it unacceptable to blow things up to force my religion on you or vice versa.
Since Islam has a political stance, and it is in direct opposition to our way of politics, I see few options other than addressing it as a political movement and banning it as we would any other political movement dedicated to the overthrow of the constitution.
If this were a new age cult, where their method for overthrowing the current order was limited to group prayer, or suicide while waiting for the mother-ship, I'd give them a pass. They aren't, and they don't.
When they break one of our laws, we lock them up.
The law enforcement approach does not exclude the war making approach. We can and should enforce all the local laws. In addition, we may need to destroy some of their countries. But extraterritorial war is outside the rights of American citizens spelled out in the First Amendment, which apply.
If we got to the point of a declared civil war internally, I trust we could suspend the whole of Constitutional Rights for the opponents of the Constitution. Their rejection of it would make it not apply to them. Death by bullet would be fine.
In the mean time, let's not go suspending the First Amendment for certain religions.