All aliens used to have to register. TV used to broadcast regular PSAs reminding them to update their registration.
Any concept where one group has to be specially identified automatically leads to a wider system where all groups must be identified. There is a constitutional black hole at the center of these proposals.
Therefore I would be very wary of such laws or procedures, the term “slippery slope” is applicable for certain.
There is also the constitutional question of group guilt for individual crime to be considered here. Once again, do evangelical Christians for example wish to open that door? How about libertarians if they are all to be guilty of any one tax evader’s wrongdoing?
The situation is not so dire that any of this is needed. Surveillance of target mosques, sure, with appropriate judicial oversight. Immigration control, yes. But taking a whole group of citizens and putting them in this sort of separate legal stream is (for lack of a better term) anti-American. And yes, it would come back to bite hard, don’t ever give the left precedents they can use against you later.
Now they just register to vote.