It's clearly within the rights of a private company to do so. What makes you think otherwise?
A Private company cannot tell you what you can do in the privacy of your own home. If they tell you you cannot sing "America the Beautiful" on the front porch of your house, do you have the right?
So as long as I am not in the Gov't , I can suppress YOUR free speech? If your company (assuming you worked for some org, not self-employed) says you cannot post on FreeRepublic, then it's OK to suppress your speech?
It's clearly within the rights of a private company to do so. What makes you think otherwise?
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Indeed. There is no "suppression" involved. If one does not accept this condition of employment, he or she can move on to a place more compatible with them, or become self-employed (at which point they will answer directly to their customers, rather than through an employer's cushioned setting).