The defects seen in inbreeding are typically not mutations. It is the result of combining DNA that is too similar.
All of us have some bad genes but most are not expressed unless there is a matching pair on the corresponding chromosomes. A gene that doesn’t express itself without a pair is called “recessive”.
Birth defects tend to be recessive because individuals that express defects are unlikely to breed. It’s natural selection through sex selection. However, unpaired recessive genes can stay dormant for generations until an individual mates with another carrier.
In inbreeding, you are far more likely to get pairs of these bad recessive genes since the mates share a percentage of DNA. Once paired, EVERY bad gene is expressed. With compounded inbreeding for generations, it becomes a nightmare. I can’t imagine how the latest generations of this family looked...
Humans (and most animals) are generally hardwired to reject incest and seek “exotic” mates because those individuals who didn’t do so were selected against. “Opposites attract” “good girls like bad boys”, “I can’t date you, you’re like my brother”, etc
This family may simply lack the natural aversion to incest and isolated themselves from others to avoid ridicule.