Nothing on that page supports what your claim.

In reality even permanent residents could be deported for what would be 1st Amendment protected activity for citizens.

In Harisiades v. Shaughnessy the deportation of legal residents for membership in the Communist party was upheld as Constitutional. This hasn't been overturned or narrowed and remains good law today.

Whether current immigration law allows for this I don't know, but this isn't a 1st Amendment issue based on current precedent.