http://www.sss.gov/FSbenefits.htm
FEDERAL JOBS
A man must be registered to be eligible for jobs in the Executive Branch of the Federal government and the U.S. Postal Service. Proof of registration is required only for men born after December 31, 1959.
I am aware of the law. I just doubt it applies to elected office, which isn’t a “job” in the full sense of the term.
Do you seriously think it’s a good idea to give Congress the power to add more qualifications to those in the Constitution? Perhaps they could pass a law saying only men are eligible, or only women. Or only people under 5’ tall.
Why not? If they can require SS registration to be president, they can require anything else not specifically prohibited by law, such as a religious test or racial discrimination.