The US has for centuries banned numerous religious practices, e.g. virgin sacrifice. No court has reversed or, in my opinion, would DREAM of of reversing such bans.
Therefore, the fully Constitutional and precedent-oriented way to go about this is to pick out specific ''Islamic'' acts and practices that are unlawful already if not performed under the aegis of religion, and ban or otherwise make unlawful these assorted practices specifically in all cases.
Wouldn't be too difficult to persuade one hell of a lot of Islamists (a small redundancy, sorry) to boogie on out of here. Just a matter of picking the right practices to ban in order to annoy them sufficiently.
Good thinking.
The Tenth Amendment has been pretty much reversed by the courts. The Tenth Amendment does not mention the Democrat Party or Socialists by name; but it would ban all of their practices (at least at the federal level) if it were enforced.
There's probably enough in The Constitution already to ban the aspects of Islam that are incompatible with civilization as we know it. The Mohammedan government of Turkey was actually mentioned by The Founders (in the Federalist Papers, as I recall) as an example of the kind of thing The Constitution was trying to protect us from. As with the Tenth Amendment, the trick is to get the courts to obey it.
I agree though, that banning practices rather than named entities is the only way that makes sense. If we outlaw "Islam", they'll just change the name. (If the Tenth Amendment outlawed "socialism", the socialists would change their name to something else--like "progressives".)