Your reference to Hitler's action puts an uncomfortable fact on the table. It suggests we have a natural obligation to avoid allowing them "to get the rule over us", although that is essentially what Hitler attempted to do for his Germany.
We also have a natural obligation to not address the question in the way chosen by Hitler. So it appears sooner than later we must formally recognize that Islam is not a religion as contemplated by the founders but is rather a cult.
The distinction hinges in this case less on beliefs themselves and more on behavior — especially transparency, accountability, and respect for individual autonomy. The freedom of religion contemplated by the founders was centered on one's right to choose what they believed but did not necessarily provide immunity for behavior of the believers.