Oh boy. I was born in a totalitarian country. It saddens me that people are happily making the same mistakes.
The dichotomy between the government and private institution you (and many libertarians) present doesn't really exist. Your rights are something that you cannot sign and trade away.
The reason why free speech exists (as a concept) is that so you, as an individual, could freely discuss wrongdoings and bad practices without fear of retribution. The idea is, ability to discuss these things leads to more efficient society. And this is true regardless whether the subject of criticism is the state, or any other institution, or any other human, even.
In your argument, somehow, you forgot the reason, why you have free speech. And so had been tricked into thinking that it is less valuable (because you don't understand its value), and you are willing to trade it away. Don't be that stupid.
Your employer can disallow you to carry a firearm on their property. You can sign a confession. You can let them search without a warrant.
I guess I question your belief that you can't trade your rights. I am not saying you should, but it appears you can. You can even waive your right to a speedy trial.
And yes, I mean people should stand for it, of course it's not guaranteed. At least, they should educate themselves about rationale behind human rights, so they wouldn't foolishly trade them away for nothing.
Actually the parent poster was right. The US constitution does not directly apply to the citizens - it defines the role and limits of government power. It was my mistake to say such agreements between people and companies should be unconstitutional. Those are details though, and I mostly agree with the rest of your comment.