I find nothing wrong with incest. Sure, it isn't something I'd do, but the way I think, victimless crimes should go unpunished. Besides, it's not like incest is something that isn't natural, humans are one of the few animals that don't regularly engage in incestuous relationships.
And before you bring up the topic of chances of deformed children, let me bring up two points.
a.) In the modern day, sex =/= having children.
b.) While, statistically, it is more likely your child will have genetic issues due to inbreeding, it is still UNLIKELY. Very unlikely. Barely any more likely than if you weren't related (if the incest only occurs over one generation). The way it works is every single human being on the planet probably has a serious genetic flaw somewhere in their genome. Everybody. That includes you, it includes me and it includes Barack Obama. There's so much genetic information that the chances of something going wrong in there are massively high. The thing is, each cell contains two pairs of every chromosome and the genetic flaw that is in one of those chromosomes is recessive, meaning it isn't expressed and the correct gene in the other chromosome is expressed. As you are genetically similar to anyone in your immediate family, there is a small possibility they inherited the same flaw. So if you have children with them, you will donate one of your chromosomes through your gametes to your child and so will your partner, meaning their is a possibility that BOTH chromosomes will have the genetic flaw meaning it will be expressed. However, this is still incredibly unlikely, and, in my opinion, not likely enough to stop two people who love each other from being together. Inbreeding doesn't really become a problem unless it occurs over multiple generations unless you are very, VERY unlucky.
EDIT: Social stigma or an individual's belief shouldn't factor into this. Why should something you find to be sickening stop other people who probably will never know from being together? The fact that people would try to enforce their own belief system and morality onto other people is what is truly sickening.