Certain religious groups can request exemption to social security on religious grounds. From instructions for IRS Form 4029:
Recognized religious group. A recognized religious group must
meet all the following requirements:
c It is conscientiously opposed to accepting benefits of any private
or public insurance that makes payments in the event of death,
disability, old age, or retirement; makes payments for the cost of
medical care; or provides services for medical care (including social
security and Medicare benefits).
c It has provided a reasonable level of living for its dependent
members.
c It has existed continuously since December 31, 1950."
RE2Boys