Similar problems have been reported in the Amish community, which does not practice polygamy. Just the small size and closed nature of the community is enough to cause rare genetic diseases. The FLDS community is extremely tiny from a genetic perspective when you only count the men.
i live a few miles from a huge Amish community. Big time genetic defects. Most they can’t even identify. They just know that “somethin’ ain’t right”.
The Hutterites, another closed community religious sect prominent in the Midwest and Central Canada, have a similar problem. The sect descends from a core of less than 400 original families and almost exclusively marriages are within their group. They live in farming communes called “colonies” and the usual practice is to exchange young unmarried adults between colonies to avoid close genetic intermixing. However, given the small size of the initial gene pool and the almost non-existent conversion of outsiders to their religious way of life has assured an increasing incidence of genetic disorders.