NO! The sovereign authority of states is specifically limited by the Fourteenth Amendment. The First Amendment, applied against state action through the Fourteenth Amendment, protects intimate and expressive associations as speech as the Supreme Court has held, "Association in that context is a form of expression of opinion." The regulation of marriage is the regulation of speech. There is NO escape from this for the states unless a large body of Supreme Court precedent is overturned. The establishment will tell you otherwise but the establishment is made up of powerful entrenched interests who receive massive profits from the false 19th Century belief that states have a free hand to regulate the intimate and expressive speech and association of marriage.