This is a fundamental problem with Muslim immigration. Islam is incompatible with the Constitution. Yet, the Constitution mandates that we practice freedom of religion.
Asking a Muslim immigrant to take an oath of loyalty to the United States -- which we do, in the naturalization ceremony -- is a meaningless exercise, given the practice of taqqiya.
At the same time, radical Islamism isn't going to go away. It's built into sharia law and the Koran -- it's part of the belief system. Islam has fought to impose itself upon the West for over 1300 years. Absent a "reformation", it's not going to give up.
At some point, this unending conflict will have to be resolved. Given the availability of weapons of mass destruction, that resolution will probably have to be sooner rather than later.
The bloodletting will be immense...