incest has a blood relation and serious concerns regarding inbreeding
But genetic testing can be used to rule out birth defects. Furthermore not all couples want to have kids. Suppose a brother and sister want to get married and are sterile (either naturally or due to surgery, like a vascectomy). Does that mean they have a "right" to marriage?
Finally, there's the fact that, under current constitutional jurisprudence, people have a right to procreate regardless of the possibility of birth defects or a genetic history of particular illnesses. Combine that precedent with the arguement that marriage is a right that can't be abridged and there's not much rationale left to ban incest.
polygamy requires multiple partners.
That's a distinction without meaning. In both gay marriage and polygamy the argument is that consenting adults have a right to marry whomever they want and that the government has no right to regulate private conduct in the bedroom.
Explain how a court can say gay marriage is harmless but polygamy is dangerous, especially given that some cultures practice polygamy.
At best, you might get one of those "but polygamists are crazy cultists who often marry underaged kids." And that is probably true in some cases. But an argument could also be made that some gays abuse kids also.
So, again, it's a distinction without meaning.
Those kind of meaningless distinctions, in the realm of courts, typically lead to either the ruling being overturned (and the matter returned to the legislature) or expanded in ways that weren't intended.
