If you were to make a general rule, it's saying if you want employment then don't say anything online, period. So it is in fact depriving any employee the right to speak about things publicly all the time. It's like putting a muzzle on a dog so he does not bark. If that's not slavery I don't know what is.
As for right to employment, well how far can you push it. And how does that not violate white privilege principles or corporate privilege principles. We have a corporate class which holds most of the wealth and if you say anything you will lose the right to make a living. That smacks of privilege, in fact white privilege.
Only the corporate class may speak. It's not sound in any way.