Not at all. It is remarkably simple to refute the argument in the title by accurately noting that skin color is morally neutral while sexual behavior is not.
But there is another interesting argument that goes even further, and it highlights how the pro-same-sex marriage crowd is actually the one similar to the racists who opposed interracial marriage.
Here’s why: The Left is (successfully) lobbying for coercive government force to change the meaning of marriage. The racists changed it to mean “only same-race couples” instead of just a union of one man and one woman, and the Left is now using it to change it to mean, “not just the union of a man and a woman.”
Marriage is what God defined it to be. It describes a thing — a union of a man and a woman. The term didn’t pre-date the institution, such that we get to define it any way we like.
If anyone is behaving like those that opposed interracial marriage it is the Left. They are the ones abusing the original and obvious definition.