Section. 1. Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
That doesn't stop two people from forming a union. The laws of the several states used to prevent perverse unions but an unconstitutional ruling from the tyrants in black changed that. (Which is why we need a federal marriage ammendment defining marriage as the union of one man to one woman. It would restore states rights)
So we have the right to be married (and always have and always will) but we do not have the right to have that marriage recognized.