They have something better, a gene clinic
They may shun cars and televisions, but it seems they really dig genetic engineering
"For generations, the Amish and Mennonites, descendants of Swiss and German Anabaptists who settled in Pennsylvania in the 1700's, have suffered from unusually high rates of dozens of genetic disorders. The diseases occur because the communities arose from a small population of founders"
As I said, the problems they face today are due to faulty genes which they inherited from the founding generation. With proper genetic screening, healthy embryos could be chosen and within a generation their genetic problems would be solved. The faulty genes the Amish have been dealt could be filtered out of the population.