"It's complicated. Lets just say that it has to do with the full faith and credit clause"
The full faith and credit clause is not really complicated and you described it well. But the more fundamental question that needs to be asked here, which never is, is why have we let government define what marriage is in the first place.
One can ascribe all kinds of esoteric and religious meaning to marriage but when you cut through the hype marriage is nothing more than a contract, legally speaking that is. So the fact is that no American has a right to marriage, they must seek permission from the state.
That is the issue that should be of concern to all freedom loving Americans.
No American has a right to have their marriage recognized by the state. For instance if you are homosexual there is nothing stopping you from getting "married". But for purposes of determining rights and obligations in regard to property and child custody and taxes, the state has the right to define what is or is not a "valid" marriage. Every state has laws prohibiting polygamy and incest and many states have instituted laws prohibiting marriage between members of the same sex (it was more or less presumed for the last 10,000 years). But the courts have been undermining the right of the people to define marriage and have usurped the power to redefine what is a valid marriage, which is the perogative of the legislatures.
Now that the threat exists that the courts are going to find some constitutional right to make the states recognize illegal marriages or invalid marriages and then force that right on other states, it appears that the only way to prevent such a travesty is a constitutional amendment.
The Constitution was designed to be amended for just such a purpose. Polygamy and Homosexuality should not be "official sanctioned". They are unhealthy lifestyles that are both physically and emotionally harmful and put unnatural burdens on children that should not be encouraged or ratified by the government.