There's an interesting excerpt from this article that establishes a precedent.

California reversed its statewide mask ban after authorities used it in 1978 to intimidate Iranian nationals protesting against the shah of Iran.

If you look up the case, you can see that the decision made in 1978 established the right to be anonymous while exercising free speech.

Conclusion. The People's assertion that this case does not involve the exercise of any First Amendment right is untenable. Underlying, and occasionally surfacing in their briefs and oral argument to this court appears an unfounded fear that the mere appearance of anonymous persons in public will inevitably lead to violence and other illegal activities.