While there are genetic diseases and deficiencies that are created through non-incest breeding, Incest is typically uncommon not just because it is a cultural taboo, but because we as a species (and many other mammals) instinctually find our siblings or close family members to not be sexually attractive through minute things like smell. If evolution is so against it, I believe it is a bit more serious than inheriting asthma from your father or something along those lines. 

If anyone remembers the Climate Change argument I had with Sleeping a few weeks ago involving the 200,000 dead Taiga that died mysteriously in 2015 and it was linked to climate change? It was also linked to a lack of genetic diversity due to inbreeding a few thousand years prior, which led to 2/3rds of its species becoming extinct in less than 72 hours. 

My point is, it is usually a bit more complicated that merely adding an increased chance of disease, and it could potentially be catastrophic. And it is, evolutionary speaking, unnatural and uninstinctual.