Why not? Until recently the Federal Government did it too. Until recently a same sex couple wasn't considered married to some federal departments, not? Wasn't the last same sex marriage case about IRS taxes when one spouse died, and estate taxes and/or death benefits?
As far as I'm understanding FF&C- and Frank can correct me if I'm wrong-
If State A says you're married, and State 1 says the benefits of marriage are A, B, C, and E- and you then travel to State 2, who says OK State A says you're married, and State 2 says the benefits of being married are only D- Full Faith and Credit does not mean State 2 has to extend the benefits A, B, C, and E to a married couple living in State 2 that was married in State 1.
For that matter there's nothing in FF&C that says State 2 has to decide to allow marriage itself, or provide any benefit at all to it.
I believe, in theory, a 6 million (adult, voting eligible) member cult could move to Wyoming (population ~600K) and remove all recognition of marriage from the State and local laws within a couple years. The best case recourse would be suing to get marriage recognized as one of those smoky hazy 9th amendment rights, or as a first amendment association based right.
If that were to happen, as I understand Frank's explanation of FF&C- Wyoming would tell incoming married couples- Great, you're married. We don't recognized marriage period in this State, so while we'll say you're married, it means nothing here.