Final answer:
The Full Faith and Credit Clause is the constitutional provision critical to debates on same-sex marriage, requiring states to honor each other's legal decisions which historically included marriage licenses.
Step-by-step explanation:
The constitutional clause that has been central in debates over same-sex marriage is c) Full Faith and Credit Clause. This clause, found in Article IV, Section 1 of the U.S. Constitution, requires that states normally honor the public acts, records, and judicial decisions of other states.
When it comes to same-sex marriage, the 'Full Faith and Credit' clause became particularly significant as it theoretically required states to recognize marriage licenses issued to same-sex couples by other states.
This led to the Defense of Marriage Act (DOMA) in 1996, which declared that states did not need to recognize a marriage between persons of the same sex even if it was recognized in another state.
However, all this changed with the Supreme Court's ruling in Obergefell v. Hodges in 2015, recognizing the fundamental right to marry for same-sex couples under the Fourteenth Amendment, rendering the 'Full Faith and Credit' matter somewhat moot in this context.