Married, not married
In many states it is illegal to marry your first cousin, but in some it is legal. Suppose you married your cousin in a state where it is legal, say New York, and moved to a state where it is illegal, say Utah? Would your marriage be legal or illegal? What if you had children?
Thankfully, states generally recognize marriages of first cousins who are married in a state where such marriages are legal; otherwise, there would be chaos in our highly mobile country.
Yet if a legally married same-sex couple with children moved from New York to Utah, their marriage is dissolved. Think of the chaos for that family, the children learning their parents are no longer married.
You may not like same-sex marriages, and you may not like first-cousin marriages, but in both cases it's wrong to wreak havoc on these established families. It's not as if the children are going to suddenly get new parents.
That Utah doesn't recognize a couple's same-sex marriage doesn't mean it's dissolved; if they later moved to, say, Iowa, they'd be legal again.
Utah's ban on existing, legal same-sex marriages isn't moral; it's just mean.