Okay. But I'll bet the OP was considering all incest.
What makes you think that? Recessive and dominant genes act the same regardless of what mammal we're talking about. In terms of breeding, the same considerations and precautions apply whether it's dogs, horses, cattle, gorillas or humans (if one were specifically breeding humans).
Yes, I've read articles about that couple. We understand genetics better now than throughout social history, and many genetic problems can be predicted and screened for, so except for the 'ick' factor and the question of coercion/rape, it's hard to defend laws against incest.
Royals are often pointed to in conversations like this, for good reason. But in reality they were no more genetically inbred than many small populations throughout the world. If you look at small island populations anywhere, inbreeding was inevitable.
My family, for example, both maternal and paternal lineages stem from a small island off Scotland in the 1850s. Like many small islands there, most people did not travel much and usually married someone in the community, and since that was the case for many generations, of course they were all genetically close - small gene pool. Four of those families immigrated here, settled in an isolated farming community, and continued as usual, with an even smaller gene pool. When I look at my genealogy, there are multiple relationships between any two people - they will be second cousins, fourth cousins, third cousins, depending on which ancestor you draw the line down from.
There are a few genetic consequences (inherited heart problems, tendency to diabetes) which are being diluted by the current generations, who have a much bigger gene pool to choose from. But it is further proof that you cannot just assume that inbreeding will inevitably end in idiot or disfunctional offspring.