They can choose not to get a social security number like anyone else, but the real exception is that they can take a religious exemption to paying social security while basically most everyone else who is of a religious organization objecting to social security past X date (I think around 1960 from memory) cannot ( I suspect this is unconstitutional religious discrimination against later forming religious groups, if I were rich I'd challenge it). However there are a couple other groups -- preachers can exempt themselves as can members of the railroad and a few other industries that have been heavily entwined with government and provide their own pension plan.