No, even on the job, they have the right, they can not be arrested for protesting at work.  But, their employer can have rules of employee conduct that say that they can not protest at work, and can be fired or fined if they do.  AND more importantly in this case, the people who pay the employer's bills have the right to not give that employer money if they disagree with employee conduct, which for most employers causes that conduct to become prohibited in the rules.