First Amendment does not cover broadcasting social security numbers.
States have laws on the books protecting individuals.
What law would prevent MSNBC from disclosing SSNs for non-fraudulent purposes?
First Amendment gives the highest protection to political speech. Much less protection to commercial speech and no protection to speech that is in furtherance of a fraud.
Releasing someone’s SSN has no legitimate purpose which could be served. The only intent that can reasonably be inferred is the intent to defraud. Thus, no protection.
Not all speech is protected speech. You can’t yell “Fire!” in a crowded theater either.