It's not that it has support, per se, it's that all of the arguments against it can be shown to be faulty or inconsistent with previously accepted principles.
The only argument against it that holds any water is the potential for genetically unhealthy children, but as the OP mentions, the government does not regulate other couples' reproduction on the basis of their genetic risks, so it would not make sense to do so for consenting adults who happen to be related.
It's an issue where every gut feeling we have says it's wrong so it can be difficult to even entertain the philosophical arguments about it.
Me said:But, a person with a high chance of passing genetic defects will suffer from this condition regardless of their partner. In this case, the chance of passing the defects is entirely because the choice of partner.
One is afflicted by a condition, the other is driven by a choice.