The main reason for their exemptions is their demonstrated track record of self-sufficiency. They have a very strong sense of taking care of each other - there

The main reason for their exemptions is their demonstrated track record of self-sufficiency. They have a very strong sense of taking care of each other - there are no poor people in Amish communities. So the courts allowed them to opt out of Social Security, because they have shown they provide their own. Similarly with education - their system works with only a minimal formal education, so the courts were happy to leave them be at that point.