At the heart of the moment for the later is an effort to change what the purpose of marriage is (or, perhaps, recognize a change that has already happened).
Specifically, the move to support gay marriage requires changing the idea of marriage being a relationship primarily concerned with natural procreation into one centered on the expression of romantic "love". You'll note, for instance, that Google is calling its campaign "Legalize Love".
The reason the state has opposed incest is that inbreeding leads to a much higher rate of birth defects.
But if marriage is shifted in focus from being primarily about creating an ideal situation for natural procreation to one based on "love", who is the state to say that two direct relatives are or aren't in "love" with one another?