If it isn't explicitly not protected though, there could still be a fun case to deal with.
The correct play here, is to get the word out that people need to review every single paper they sign and line out the clauses that allow dismissal for bringing yourself or the company into public disrepute. People have to understand that they shouldn't be just signing away their rights like that.
The ACLU can't protect you if you've signed these kinds of contracts.