In an effort to make the Church look bigoted and hateful, LGBT activists often compare homosexuality with interracial relationships. It is argued that the Church's disagreement with gay "marriage" is morally equal to past hatred of interracial marriage.
But setting morality aside for a moment, there is a major difference between interracial relationships and homosexual relationships: functionality. Supposed differences between "different" races are trivial at best. It's not like a white man can only make babies with a white woman. But a homosexual couple can never produce children. It's biologically impossible.
LGBT activists tend to respond to this reasoning by asking about infertile couples. But morality is never based on an exception, it's always about the rule. You can't say "my charger is broken, therefore it's perfectly valid to have two chargers and no phone." I can't play Angry Birds on a lightning lead. I need an iPhone for that. In the same way, although there are straight couples who can't have children, children can only be produced by straight couples.
When the Bible defines marriage, it defines it as when a man leaves his father and mother to be joined to his wife, and the two shall become one flesh (Genesis 2:24). When questioned on divorce, Jesus specifically quoted this definition and declared that this is how God designed it (Matthew 19:3-9; Mark 10:2-12). To be "one flesh" means the completion of the human function. There are many parts of the human body that can function whether alone, or even in a gay relationship, but only in a heterosexual couple can the full potential of the human body be realised.
There is no specification in the Biblical definition of marriage that says two people with different skin colors are incompatible. Similarity in values is strongly advisable, but there is no prohibition in the entire Bible on interracial marriage. Jesus even has some mixed couples in His own genealogy, and Moses notably married an Egyptian woman. But there are multiple prohibitions on homosexuality in the Bible, and the definition of marriage ultimately means you can no more marry someone of the same sex than you can marry a tree.