Interesting that you specifically requested a liberalist opinion... although I guess I can see why. In that case, I got one for yoy
Although it has effectively been voiced prior, I'm part of the "If there's mutual consent- there's nothing wrong with it" train of thought. I agree with you in terms of the churning of the stomach re: Incest (although your definition of 'normal' seems rather narrow), but similar feelings are evoked from the idea of homosexual relations, but I have no problem with that whatsoever. While I may find both of these concepts rather disgusting, far be it fair for me to prohibit something because I don't like it.
You basically hit the nail on the head with your "I can't give reasons why" idea. It's just a feeling of (for lack of a better term) ickyness. I totally agree. But it's not our place to act on it. I don't agree with incest- so I won't participate in it! To stop other people from doing it as well is wrong. But I stress again- consent. Which does mean children can't be involved given that the legal age of consent is 16- an age I personally agree with.