Profile? Sure, that’s just good police work and protection.
Deport US citizens based on their religion? That crosses the line.
No, you’re right... an American citizen by birth is an American citizen. We can’t make people stateless.
But we can, as you say, be on the alert.
Being born here is of no consequence if you raise your hand against the country and say "Death to America". Islam is incompatible with the American way of life.