States can change their own laws to recognize whatever they want.
It's a double edged sword. Yes, states are free to have their own laws, but they are not free to force their laws on the other states.
The standard procedure is to recognize marriages/unions from other jurisdictions unless there is legislation specifically to the contrary (eg, State A gay-marries Ben and Ned, Ben and Ned move to Arkansas which has legislation banning gay marriage, so their marriage is not recognized in Arkansas).
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