Originally Posted by rocket88
Question: "if you move what is the status of your marriage?"
You remain married because the license was issued and remains valid in the jurisdiction in which it was issued. The marriage remains valid, it's just that the new state doesn't recognize it. To end the marriage either a state court would have to issue a divorce (which would require the new state to recognize it as a marriage to begin with - a Catch 22) or it would have to be annulled in the original jurisdiction. Simply moving doesn't annul a Civil Marriage.
Question: "Can you just change your official residence for a couple of months as a backdoor divorce?"
Moving (or returning to the new state) isn't a "divorce" or "annulment". The marriage remains valid, for example a couple from Mississippi go to Massachusetts and gets a legal marriage and then returns to Mississippi. Mississippi doesn't recognize the marriage but the couple still gets federal recognition and submits their tax forms as "Married Filing Jointly". If their Civil Marriage was annulled by simply setting foot in Mississippi, then they would have no Federal recognition.
Question: "Why does a state get to say "we recognize this marriage from another state, but not this one" just because of sexuality."
At this point in time, because Article IV, Section 1 gives Congress the power to determine the "effect thereof" of public acts between the States. Congress did that in 1996 by passing the Defense of Marriage Act and in Section 2 stating that States are not required to recognize Civil Marriages from another states for same-sex couples. Now whether that provision is Constitutional or not is another question since it relies on the gender classification of the couple. However the SCOTUS has not had a case where they have ruled on Section 2, Windsor only impacted Section 3. Now if Congress had said that States were no required to recognize ANY Civil Marriage that conflicted with their own internal laws, then that would have been 100% Constitutional.