Just because you retain the right to say F U to your government doesn't mean you have the right to say F U to your employer's customers while acting in the context of such employment.
What they don't have is freedom from consequences. They don't have imnunity from being fired.
A government official used his position of power to get a critic fired over a personal insult.
I'm not sure what "free speech" is good for if government officials can just get you kicked from your job for exercising it.