The question is in regards to states disclosing information about gun licensees.

From The Volokh Conspiracy:

There is no First Amendment right to access government records. There’s a First Amendment right to speak about what you’ve found in a record that was released to you, but not a First Amendment right to access the record in the first place. (Courts have recognized one significant exception this principle — a First Amendment right of access to documents filed in criminal prosecutions or civil lawsuits. But that exception is limited, and not applicable to ordinary government records.)