Many of the secular universities in the U.S. were originally Christian schools (Harvard, Duke etc etc.) and all of the older schools had some religious affiliation including Columbia with the exception of UVA which I believe Jefferson started specifically to have no religious affiliation. (Jefferson also re-wrote the Bible to his own standards) There are I believe, two secularized former Catholic colleges in the United States and several that are Catholic in name only and would probably be more honest to just stop calling themselves Catholic.