It's common for many to compare the topic of same-sex marriage with the issue of interracial marriage - that is, advocates of same-sex marriage will compare their opponents with those who vehemently opposed interracial marriages in the 1950's and 60's. While popular in many circles and parroted uncritically in social media, this argumentation has some faults.
Firstly, it's just an empty personal attack. "Oh, you don't agree with me?! Well, you're just like a racist!" In some ways, it's no different than Godwin's Law: you're in essence going to an extreme example to broad brush your enemies and write them off to others as "the bad guys," all without addressing their arguments. It might also be worth noting that racism tends to stem from the belief that a person of another race is a lesser or subservient human being; while there are those who treat homosexuals in a similar manner, the large portion of those who oppose same-sex marriage do so not because they see homosexuals as lesser beings or non-citizens.
Secondly, homosexuality is something you can hide - race isn't. Barring any skin condition outside your control, you can't hide being a black person. To paraphrase one black comedian: "You gays have a closet you can go in and out of - I don't!"
Thirdly, the issue of America's racial tension is different than that of her homosexuals, and it's unfair to try to tie the two together - if not a bit extreme. It's a bit like how some people, upon hearing of some persecution in some country, immediately jump to the Holocaust as an example, essentially comparing any persecution or a killing of any group of people to the Holocaust, even if the situations or motivations are entirely different. To paraphrase a black scholar I once heard on CSPAN: "While I sympathize with homosexuals, I don't like it when they compare their cause to the civil rights movement - Ellen Degeneres never had to pick cotton at the crack of a whip."
Fourthly, the question of whether or not a black man could marry a white woman was a matter of whether two races should marry...it did not redefine marriage as an institution. A black man and a white woman together still function as husband and wife the way they should in marriage, and the man and woman still function in their roles pertaining to the individual genders. Same-sex marriage, on the other hand, completely redefines marriage and the roles normally played by the genders in a heterosexual relationship. It forgoes the effect the genders have on one another, the ability for the two genders to reproduce together, and the roles the two genders play in the raising of children. Ultimately it turns the definition of marriage into emotional satisfaction between two people - a shallow foundation at best (and one that, inevitably and logically, opens the door for things like incestuous relationships).