In my opinion, animals "work it out" by the weak ones simply getting killed. They don't seem to avoid incest, I used to go to the same place on vacation for years, and I saw a cat give birth to a litter, and the next year I was there the male kittens (now cats) were having sex with their mother and/or the female kittens (now cats).
There were a lot of cats, but after seeing them being born and growing and actively look for them, I'm pretty sure we were not mistaken that they were the same individuals.
A possibility is that you are less fertile with someone who is close to you in genes. Another thing is that the egg only lets in a sperm that is as different as possible, so it takes generations of inbreeding before any complications occur.
So the potential inbreeding in that culture really wouldn't be a big problem, it was simply something that came to mind when thinking about it.