I'm talking about rights, not laws. Congress could, for example, pass a law requiring immigration officials to give certain process to people denied visas. Judges could enforce those laws, and nothing about such a scheme would violate sovereignty.[1] But saying that foreigners have a right to such process is different. Where does this right come from? Foreigners are not parties to the Constitution so it can't come from that. It has to come from something "bigger," some higher law that encompasses both the foreigner and the U.S. But unless you believe in some sort of God and divine law, there is no such thing. The sovereign entity is the end of the line--nothing binds its actions other than its own conscience.

[1] Though many people would say it's a separation of powers violation.