While public employees typically have greater protections on the job than employees working in the private sector, they don’t have unlimited protection from interference with their jobs.
Recent case: John, a tenured professor at a public university, holds controversial views on the relationship between autism and vaccinations. He wrote a textbook on the topic that he wanted to use in his classes. The university turned down his request. He was, however, allowed to use his book as a supplement.
He sued, alleging deprivation of his free speech rights.
The court tossed out his lawsuit, reasoning the university had a right to set the textbook for its courses. Plus, since John was still free to use his work and voice his opinion in the classroom, he was not prevented from speaking freely. (Oller v. Roussel, et al., No. 14-31101, 5th Cir., 2015)