If you are referring to the first amendment, that protects us from government censorship. There are a number of ways we may agree to censor ourselves when interacting with private entities. I signed a non disclosure agreement with my employer. I agree not to create photos of expos I enter. And so on. It seems excessive, but it's legal to stipulate it.
Just curious, if you discard the legitimacy of private profit, is it ever legitimate to silence employees? I'm skeptical but I'm open to a good argument.
Most of the time the agreements I hear about are basically to guarantee that private corruption will go unpunished.