And yet, this is what free speech means - your employer can fire you if they don't like what you say. They don't have to justify it; they don't have to apply rules evenly. Unless it's for an illegal reason, your employer can fire you if they don't like your self-expression. That's them excercising their freedom of expression.
"In most non-government employment situations, unless state laws provide additional protections, your work has wide latitude to curtail your speech or punish you for it. For example, although a police officer cannot arrest you for wearing a hat with a political statement on it, your boss may well have the right to fire you for it."