Well someone on the right might think that the laws banning interracial marriage conflicted with the traditional definition of marriage. That those laws were just a contemporary society trying to redefine something that shouldn't be redefined. That marriage is between a man, a women, and god (if you believe in the 3rd one).
The big difference between the two is that banning interracial marriage was done by design. To enforce a social norm on society that might resist at the micro level.
The idea of marriage as being between a man and a women wasn't designed to exclude people in same-sex relationships. It wasn't designed at all, it just happened across cultures, societies and time. Marriage was just what people did before they essentially had children, etc. in order to place legitimacy on the relationship and children.
The people arguing against same-sex marriage would say that it would damage the institution of marriage, if true would be a reason not to permit it. I am unconvinced that it would be so I believe it should be expanded to include same-sex relationships. However, not by a handful of individuals in powerful positions. It should have happened in the democratic process. Not quick, not pretty but once done legit.
Let the balkinization of America begin.