Public employees retain free speech rights under the First Amendment and can’t be punished for speaking out if they do so as citizens and not in their role as a government employee.
Recent case: Keith was a manager for a public waterdistrict. Upon returning from vacation on one occasion, he learned that the district was considering being annexed by another governmental unit. Keith spoke with members of the public who were also water customers and urged them to attend council meetings to protest the potential annexation, arguing that it would be bad for customers. Some did attend.
When Keith was terminated for telling them about the potential deal, he sued, alleging he had spoken to the customers as a public citizen concerned about an important public issue. The court agreed that Keith’s communications were protected speech. (Hardesty v. Cochran, et al., No. 14-3114, 5th Cir., 2015)