I think we're actually having different arguments. :-)
Yours, as I understand it, is that islam is incompatible with the concept of Biblical law and Natural law as well as the Constitution. This I both understand and accept as truth.
The problem is is that the Constitution doesn't sit in judgement of anyone's beliefs. It leaves one's beliefs in the realm of one's conscience, and it's ability to impact someone can only be outside of that.
Of course, if a terrorist actor comes from a particular mosque in the US, that mosque should be closed and all its members investigated. Countries that have terrorists in them should have ALL of there citizens evicted from the US and no citizens from those countries should be allowed in.
There are some perfectly Constitutional remedies to reduce the barbarian horde, and we always have the last recourse in a judicious application of the second amendment.
No, it was a legal argument. By adopting the Shahada they have declared themselves not to be a party to the social contract that is the Constitution; they are not among "we the people." They are not "people of the United States," because Islam does not recognize the United States as a nation. They are therefore dedicated on penalty of death thereby to the destruction of the very existence of the nation, as a global caliphate would not permit such to exist. That makes them literally a declared enemy of the United States.