Comment by dmacedo
Not American here, but I'm aware of both privacy in mixed forms (privacy act 1974, HIPAA, COPPA, and CCPA in California); as well as anonimity in First Amendment et al since there's case law (IANAL) demonstrating the requirement of anonimity to avoid persecution of free speech.
All of these have limitations and exceptions in a complex legal system. But to issue a blanket statement like the comment above is no really correct - just trying to make a point, I guess
Also not a lawyer but anonymity case law is a mixed bag to best, and more practically speaking very narrowly targeted compared to privacy.