But does this really follow? Does the full faith and credit clause allow a state to "export" its marriage laws?

Such logic surely has not been followed when "full faith and credit" is applied to any other subject. For example, in 1997, the Supreme Court ruled in the case of Nevada v. Hall that, "The Full Faith and Credit Clause does not require a State to apply another State's law in violation of its own legitimate public policy"....".1 Similarly, in April, 2003 the Court stated in Franchise Tax Board of California v Hyatt that, "The Clause does not compel a State to substitute the statutes of other States for its own statues ...".2 In these and numerous other cases, the Supreme Court has made clear "full faith and credit" means that states must recognize contracts and court settlements and the like from other states, but only as long as they are consistent with the states own laws and policies.

Suppose that some chemical used in industry was found to present a health hazard. Suppose that, say, New York responds by completely banning the use of this chemical, while Pennsylvania decides that the appropriate solution is to require anyone who uses this chemical to have a special license, presumably not issued until after they demonstrate that they can meet various safety standards. This is surely not an outlandish scenario: States have such differences in their legal response to various situations all the time. Now, suppose that someone who has a license to use this chemical in Pennsylvania moves to New York. Does the full faith and credit law allow this person to use the chemical in New York, even though New York law explicitly prohibits its use? Is New York obliged to recognize the Pennsylvania license? I strongly doubt that any court would take such an argument seriously. And if a court did force New York to recognize it, surely the New York legislature -- if not the populace in general -- would be outraged. Even those who didn't like the original law would probably be angry at this imposition on their right to make their own laws.

Simple logic would say that the same principle would apply to homosexual marriage. If one state changes its laws to provide for such marriages, that is presumably their legal right. But two men married in that state would not carry that states law with them when they moved to another state.