The state has an interest in seeing to it that minor children are not married, and that bigamy is prevented.
Otherwise, any two people should be able to get married provided that both are single and willing.
Marriage between "races" was a minority opinion in most of the South until it was overruled by the Supreme Court. It might still be a majority opinion in some states.
This is not an issue that should be decided by the majority, because the majority is unaffected by it. The effects of gay marriage have far fewer visible consequences than interracial marriage, after all. You cannot tell the child of a gay marriage by looking at him, after all. In the case of an interracial marriage, you can at least some of the time.