Internal Revenue Code section 3121(b)(17) provides that the Social Security tax does not apply to wages from any:
"service in the employ of any organization which is
performed (A) in any year during any part of which such
organization is registered, or there is in effect a final
order of the Subversive Activities Control Board requiring
such organization to register, under the Internal Security
Act of 1950, as amended, as a Communist-action organization,
a Communist-front organization, or a Communist-infiltrated
organization, and (B) after June 30, 1956."
This provision was added in 1956 to the Internal Revenue Code, in order to deny Social Security retirement checks to the much-feared Communists. Naturally, the Communists were not required to pay into Social Security either.
Congress was particularly irked by a 1955 Washington Daily News article entitled "Red Inmate Gets $88.10 Monthly Security From Hand He Tried to Bite," about a 65-year-old Communist serving a three year prison sentence for conspiring to overthrow the US government, who received Social Security checks while in prison and before his deportation to Russia.
(Senator John Williams complained in gender-confusing terms that all convicted felons were still entitled to Social Security, other than a "person who would thus benefit from his own crime, such as a woman who murdered her husband and thus became eligible for social security.")
What was a penalty in the 1950s might be a blessing today. Younger employees nowadays might prefer to forgo paying the Social Security Tax and give up on the fragile likelihood of receiving Social Security checks in their retirement. The employers would also save some money on their Social Security contributions.
Unfortunately, it is currently unclear how to register one's employer as a Communist-front or Communist-infiltrated organization. The mandatory registration requirements of the Internal Security Act of 1950 were repealed in 1968 after some court cases found them to be unconstitutional. The Subversive Activities Control Board was abolished in 1972. Perhaps an employer could voluntarily send in a registration form and see how it goes.