Section 3 of doma was struck down,next up is section 2, which allows states to deny marriage rights.
SCOTUS ruled specifically on section 3.
The Full Faith and Credit Clause—Article IV, Section 1, of the U.S. Constitution—provides that the various states must recognize legislative acts, public records, and judicial decisions of the other states within the United States. It states that "Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State." The statute that implements the clause, 28 U.S.C.A. § 1738, further specifies that "a state's preclusion rules should control matters originally litigated in that state." The Full Faith and Credit Clause ensures that judicial decisions rendered by the courts in one state are recognized and honored in every other state. It also prevents parties from moving to another state to escape enforcement of a judgment or to relitigate a controversy already decided elsewhere, a practice known as forum shopping.
Article IV,section 1 of our constitution doesn't allow for states to not recognize the legal proceedings of other states.