Apparently in the 21st Century you are not eligible to serve on the US Supreme Court if you are a protestant and attended a state university.
RE: if you are a protestant and attended a state university.
Scalia — Georgetown, Harvard
Thomas — Holy Cross, Yale
Alito — Princeton, Yale
Roberts — Harvard
Kennedy — Stanford, London, Harvard
Kagan — Princeton, Oxford, Harvard
Sotomayor — Princeton, Yale
Breyer — Stanford, Oxford, Harvard
Ginsburg — Cornell, Columbia