From a press release:
Kilolo Kijakazi, Acting Commissioner of Social Security, announced that the agency now offers people the choice to self-select their sex on their Social Security number (SSN) record. The agency has implemented this policy change and the new option is now available. ...
People who update their sex marker in Social Security’s records will need to apply for a replacement SSN card. They will still need to show a current document to prove their identity, but they will no longer need to provide medical or legal documentation of their sex designation now that the policy change is in place.
The agency will accept the applicant’s self-identified sex designation of either male or female, even if it is different from the sex designation shown on identity documents, such as a passport or state-issued driver’s license or identity card. SSN cards do not include sex markers. Currently, Social Security’s record systems are unable to include a non-binary or unspecified sex designation. The agency is exploring possible future policy and systems updates to support an “X” sex designation for the SSN card application process. ...
It doesn't matter to the Social Security Administration what a person's gender identity might be. The Social Security Act is gender neutral. Wherever there's a wife's benefit, there's a husband's benefit. Wherever there's a widow's benefit, there's a widower's benefit. There's really no need for the Social Security Administration to even record gender. It's a relic from more than 40 years ago when the Social Security Act was not gender neutral.