Of course you do. You probably lost rights before then if you signed an employment contract, and your employer lost rights when they started working with the government. You lost rights the first time you registered with paypal or facebook (forced arbitration clauses.) You lost rights when you signed your lease.

I don't understand what's supposed to be shocking here. There's this phrasing that seems to indicate that this is an absurd situation rather than a commonplace one.

Yes, obviously. That's how it works.

It just seems weird to suggest that I can be like a random IT worker at some tech company and can post something like "All hate speech should be illegal" and that will be fine. Then my company signs some contract with the government and suddenly tweeting that again would result in prison time.