Hi clo,
I am not as liberal as you are re immigration. I can see the reason to prefer people whose beliefs don't undermine the secular freedoms on which everyone depends.
But even so, the US is a country full of immigrants with an immigrant tradition. Take that away as a principle and only the indigenous peoples ought to inhabit the Americas. There's not even a way to include the descendants of slaves in a justification of immigrant citizenship. Everyone would need to pack their bags. Including the deplorables.
Not that they are wanted back. You are welcome to your pilgrims! ;-)