Full Faith and Credit Clause and the aftermath of the Supreme Court marriage decisions

Perhaps I am deficient in subtlety of reasoning, but I just don't see how anyone can possibly square the Full Faith and Credit Clause, from Art. IV, sec. 1, with some states disrespecting the valid marriages of others, or the Federal government basing anything on the domicile of the married couple if they were legally married in another state.

"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."

Two small subtleties. The second sentence is conjunctive, "and," so it does not provide that Congress has the power to qualify or restrict the first sentence from having full legal force. The Congress can prescribe manner and effect, but cannot preclude the import of the first clause, which is that the "acts", "records" and "judicial proceedings" of one state are deemed valid in every other. Marriage is all of those things.