From a constitutional perspective, one might argue that the state has a compelling interest (for genetic, health-care, and social reasons) in preventing the reproductive success of incestuous relationships.
though I think you could make a legal case against producing a child from such relationships. On what grounds?
Yes and no. On the one hand, the overwhelming odds of producing an unhealthy child from an incestuous relationship are indeed of state interest; on the other hand, one could then argue that the state should test all fetuses for defects. If we're willing to legislate seat-belt use for the small percentage of driving encounters that result in accidents, then I'm sure we're willing to legislate incestuous relationships for the very high percentage of unhealthy children produced, plus the overwhelming psychological damage that it can/will do, especially on the younger party (which is not relegated to adult-minor encounters).
I don't think that the state can argue it has an overpowering interest in keeping adults out of psychologically damaging situations/relationships. It however does have an interest in minimizing genetic defects in the population. And, while in a vacuum, this argument might be enough for incest laws to pass constitutional muster (at least producing offspring from such a relationship, the court could draw a distinction between sex and procreation, but would probably be reluctant to do so because of the amount of involvement of government in private life this would entail), the state will then have to answer to the court why those with inheritable disabilities are allowed to reproduce...if this is the argument the state uses, it creates an inconsistency in policy.
At the same time, incest is instinctively repulsive, so the state will get a sympathetic ear from the court...but the formal legal arguments are going to be very difficult to make.
Should be an interesting court case regardless of the outcome. I would quite enjoy to see this one come before SCOTUS and read the ensuing opinions.