I think the alien is still protected under First Amendment in the sense that you cannot criminally charge him of a crime. It simply has a consequence as outlin

I think the alien is still protected under First Amendment in the sense that you cannot criminally charge him of a crime. It simply has a consequence as outlined in the context of INA, losing a benefit that is obviously not applicable to the US Citizens in the first place, just like a US Citizen could lose a public job (Garcetti v. Ceballos).