Apparently this question is currently under judicial review. And being hotly debated by the learned justices.
Excerpts from the dissenting opinion
[T]his Court is not a legislature. Whether same-sex marriage is a good idea should be of no concern to us. Under the Constitution, judges have power to say what the law is, not what it should be. The people who ratified the Constitution authorized courts to exercise “neither force nor will but merely judgment.
Nowhere is the majority’s extravagant conception of judicial supremacy more evident than in its description—and dismissal—of the public debate regarding same-sex marriage. Yes, the majority concedes, on one side are thousands of years of human history in every society known to have populated the planet. But on the other side, there has been “extensive litigation,” “many thoughtful District Court decisions,” “countless studies, papers, books, and other popular and scholarly writings,” and “more than 100” amicus briefs in these cases alone. What would be the point of allowing the democratic process to go on? It is high time for the Court to decide the meaning of marriage, based on five lawyers’ “better informed understanding” of “a liberty that remains urgent in our own era.” The answer is surely there in one of those amicus briefs or studies.
The truth is that today’s decision rests on nothing more than the majority’s own conviction that same-sex couples should be allowed to marry because they want to, and that “it would disparage their choices and diminish their personhood to deny them this right.” Whatever force that belief may have as a matter of moral philosophy, it has no more basis in the Constitution than did the naked policy preferences adopted in Lochner.
On the constitutional basis for a right to same-sex marriage
Although the policy arguments for extending marriage to same-sex couples may be compelling, the legal arguments for requiring such an extension are not. The fundamental right to marry does not include a right to make a State change its definition of marriage. And a State’s decision to maintain the meaning of marriage that has persisted in every culture throughout human history can hardly be called irrational.
The majority’s decision is an act of will, not legal judgment. The right it announces has no basis in the Constitution or this Court’s precedent.
The Constitution itself says nothing about marriage, and the Framers thereby entrusted the States with “[t]he whole subject of the domestic relations of husband and wife.”
Stripped of its shiny rhetorical gloss, the majority’s argument is that the Due Process Clause gives same-sex couples a fundamental right to marry because it will be good for them and for society. If I were a legislator, I would certainly consider that view as a matter of social policy. But as a judge, I find the majority’s position indefensible as a matter of constitutional law.
On the natural and historic basis of the institution of marriage
The premises supporting th[e] concept of [natural] marriage are so fundamental that they rarely require articulation. The human race must procreate to survive. Procreation occurs through sexual relations between a man and a woman. When sexual relations result in the conception of a child, that child’s prospects are generally better if the mother and father stay together rather than going their separate ways. Therefore, for the good of children and society, sexual relations that can lead to procreation should occur only between a man and a woman committed to a lasting bond.
On how the majority opinion basically requires legalization of polygamy/plural marriage
Although the majority randomly inserts the adjective “two” in various places, it offers no reason at all why the two-person element of the core definition of marriage may be preserved while the man-woman element may not. Indeed, from the standpoint of history and tradition, a leap from opposite-sex marriage to same-sex marriage is much greater than one from a two-person union to plural unions, which have deep roots in some cultures around the world. If the majority is willing to take the big leap, it is hard to see how it can say no to the shorter one. It is striking how much of the majority’s reasoning would apply with equal force to the claim of a fundamental right to plural marriage.
When asked about a plural marital union at oral argument, petitioners asserted that a State “doesn’t have such an institution.” But that is exactly the point: the States at issue here do not have an institution of same-sex marriage, either.
On what our Founders would think about five unaccountable oligarchs in robes deciding what does and doesn’t constitute marriage
Those who founded our country would not recognize the majority’s conception of the judicial role. They after all risked their lives and fortunes for the precious right to govern themselves. They would never have imagined yielding that right on a question of social policy to unaccountable and unelected judges. And they certainly would not have been satisfied by a system empowering judges to override policy judgments so long as they do so after “a quite extensive discussion.”
Viewed from a wider perspective, nothing very dramatic actually comes with this disappointing development. The encroachment has been gradual and incremental, since the initial "camel's nose under the tent".
Supposedly, the Supreme Court has spoken by choosing to remain silent. But nothing precludes revisiting the ignored appeals in the future. Until the Court issues a specific ruling, the controversy has no closure.
Nonetheless, the homosexual players have become emboldened in their sense of accomplishment, which will result in inevitable greater sense of entitlement. Predictibly, they cannot ever be satisfied with this concession or any other, but will continue pressing to “normalize” their deviance in other ways. Already, homosexual partners are anticipating the next step in legal manuvering. From a Deseret News quote, "Now that this is settled, the focus is getting adoptions done for those couples. That will be the No. 1 priority for them."
Sadly, there is no lasting happiness to be found in the false promises of such deviant behavior.
I intend no antipathy toward any individuals – I am satisfied that the legal demands have been met, despite the majority of popular voter opposition. But I have no obligation to recognize things as anything but what they really are. This is strictly a legal fiction, legalizing homosexual "marriage", not some higher moral standard.
In my view, it is not and never will represent anything to do with principles of equality. And it clearly violated democratic ideals, to have federal courts dictate what voters can approve, and have approved.
I predict that the sense of vindication and hubris will prove to be pyrrhic and ephemeral, as are the rewards of all of Satan’s enticements.
We will continue to decry and oppose the tide of evil, as with legalized abortion and other such offensive and evil abominations.
Official response from the Church as appropriate to this occasion.
I am in a difficult place, trying to reconcile the counsel for civility with current events. But it has ever been so, even with followers of Jesus in former times...
Life in the world continues…