The rules are different for the government. Protection for private employees are weaker. The government has the force of law (literally force) on its side, so what it is allowed to do is different. A private company cannot truly compel an employee because the employment contract is at-will: either side can terminate the arrangement without cause.

By that same logic the government can't truly compel either as long as they only fire the employee. Obviously the government would be in violation of 1A if they took it further by charging the employee with a crime.