If I get a job and then while on the job insult the customers repeatedly and so egregiously that they refuse to return, those insults may well be protected by my God-given and First Amendment protected rights. However, my workplace is my employer's property and responsibility. While Congress can make no law prohibiting my free speech, my employer has the right (and if he has partners/stockholders/investors may have the legal and moral responsibility) to remove a distraction that is costing the business money. Blackballing this traitor is not censorship; it's a natural consequence of bad behavior.
The rest of your post was spot on, but this part was incorrect in the context of a private employment situation.