Justice Samuel Alito's dissent is as good a sampling of the opposition's reaction as any:
Today’s decision usurps the constitutional right of the people to decide whether to keep or alter the traditional understanding of marriage. The decision will also have other important consequences.About using the decision "to vilify Americans who are unwilling to assent to the new orthodoxy", I can only snort derisively. No matter how the Court ruled, I would feel the same way toward opponents of same-sex marriage. Were I inclined to vilify them (and I like to think I'm not, but to tell the truth I'm not sure), nothing the Court could have said would have kept me from feeling that way. (Nothing the majority claimed in the Citizens United and Hobby Lobby decisions has changed my mind about their fundamental wrongness.)
It will be used to vilify Americans who are unwilling to assent to the new orthodoxy. In the course of its opinion, the majority compares traditional marriage laws to laws that denied equal treatment for African-Americans and women. E.g., ante, at 11–13. The implications of this analogy will be exploited by those who are determined to stamp out every vestige of dissent.
As much as Justice Alito might like to think the Court's imprimatur matters to public opinion, it really doesn't. Not much. By the time the Justices start considering a case, everybody who cares has made up her mind. Certainly that's true for this issue.
To the question of "vilification" and the specter of "[stamping] out every vestige of dissent", I must again snort derisively.
First: you have the right to say and to believe same-sex marriage is wrong. You don't have the right to be popular. You don't have the right to escape criticism. "Vilification" of private citizens by other private citizens is a necessary risk in a society that prizes free expression. So, Justice Alito, even if the Court's decision directly prompted that kind of vilification (which, again, it won't), tough luck.
Second: the phrase "stamp out every vestige of dissent" is deliberately inflammatory. It conjures the image of Nazis ruthlessly crushing those who opposed Hitler, of resistance to authoritarian regimes everywhere and throughout history.
That's not the situation that obtains in the U.S., nor is it likely to obtain unless the nation crumbles entirely.
Alito and likeminded souls seem to imagine that federal stormtroopers will come for opponents of same-sex marriage, but those (nonexistent) stormtroopers won't come. No, the coercion of same-sex marriage foes will come from the daily interactions with millions of their fellow citizens who disagree with them and who tell them so firmly, and, I hope, respectfully. They will feel not the hands of federal marshals, but the weight of society's disavowal of their views. Alito probably doesn't like such coercion any better than the idea of federal stormtroopers, but he can't stop it.
Finally, opposition to same-sex marriage in all likelihood will never be stamped out.
You can't legislate attitudes out of existence. You can't change people's core beliefs with a court decision. And if the struggle for equal rights in the last century has taught us anything, it's that some people will never accept that certain others are worthy of respect. A small percentage of people disapprove of interracial marriage even today; Dylann Roof is but one of many who have an irrational hatred of blacks; sexism, explicit and implicit, still haunts us in spite of all the progress women have made over a hundred years.
In light of all that, is it reasonable to expect that opposition to same-sex marriage will be stamped out in our lifetime? Of course not.
Is it reasonable for people to try to bring the opponents of same-sex marriage around? Well, yes, court decision or no. And that persuasive process would have gone on even if the Court had ruled same-sex marriage was not mandated by the Constitution and its amendments.
Alito doesn't want himself or his ilk to be subjected to societal pressure, a curious attitude to have considering that the devoutly religious (who form the majority of the opposition to same-sex marriage) are perfectly happy to exert pressure on others in service of their religions.
To that I say, again, tough luck.
Get over it.