Let's examine the First Amendment, shall we? Specifically, the part of the FA that protects your free speech rights.
This is, of course, prompted by the firing of the "patriarch" of the reality show Duck Dynasty for his anti-gay statements on GQ the other day. Right wingers are going apoplectic over it, saying that he is being stifled from speaking out.
The first thing to understand before we even start looking at this is that the Constitution is a blueprint. It is the blueprint for how our government is to be built and managed. The Bill of Rights is an addition that was added a few years later as the result of a compromise that allowed certain States to vote for the ratification of the Constitution because those States were worried that the original did not specifically lay out the rights that were guaranteed to citizens and prohibited the government from violating those rights.
Thus, strictly speaking, the First Amendment restricts THE GOVERNMENT from abridging your speech. It cannot either keep you from speaking by censoring your speech nor punishing you for speaking. Written or spoken, it doesn't matter, and some actions are also, by rulings from the Supreme Court, considered political speech, and this also protected.
Naturally, since the government cannot restrict your speech, neither can others.
But, and this is important, YOU can. You can even enter into a contract with someone wherein you promise to censor your public speech and actions so as to not reflect negatively on the relationship between you and the other party. In return, you allow that other party to take certain actions against you should you violate that part of the contract.
Which is what happened to Phil Robinson. He signed a contract with A&E, probably a standard actor's contract, and that standard contract contains a reasonable and common clause that says he must restrict his public actions and speech so as to not reflect badly upon the reputation of the show.
He then went on ANOTHER network and violated that contract by making controversial and hateful comments that did reflect badly upon both him and the show and A&E. Little wonder that they fired his ass.
His free speech rights are NOT being violated. He still has full rights to speak up and say anything he wishes, stupid or not. He just lost the contract because he opened his mouth and said something he should not have said in public. His choice, his responsibility.
The right wing IS big on personal responsibility, isn't it? Well, this is the result of his acting irresponsibly. Suck it up, big guy! Ain't responsibility a bitch?