because every side has acknowledged the dangers of inbreeding and incest.
errr, not so much
With the exception of the very tiny/minute proincest-minority that incest is fine and dandy, which side progay marriage or antigay marriage is saying that inbreeding and incest isn't a bad thing? The progay marriage side? Or the antigay marriage side? The proincest crowd is so small that statistically they're outliers in this political debate. In fact, they're so small, technically they're not a side at all.
The antigay marriage side isn't proincest. They think gay marriage is the moral and social equivelent to inbreeding. So they're using the fearmongering argument that inbreeding and incest is very dangerous and thusly any procreation during gay marriage is dangerous.
The progay marriage side is saying that gay marriage isn't at all related or similar to incest and inbreeding. They tend to use science and reason and also highlight that incest and inbreeding is a terrible thing and that the conservatives need to stop comparing gay marriage to inbred family marriage.
It's the only thing that both sides agree on. Incest and inbreeding is bad.
What other side (statistically speaking) are you referring to?