A person's personal time and personal views are theirs, theirs alone, and must be protected from their employer. The best way to keep an employee from speaking up when you're doing dirty is to not do dirty. And we, as that society that grants Amazon and similar megacorporations the privilege of (for it is not a right to exist, they aren't people) existence, should break straight in half any of them that tries to curb its employees from speaking up when that company is doing dirty.
"Shut up and be a cog." No. Do no such thing. Be a citizen and be a human, and help others do the same.
The policy prevents employees from speaking, period, if they are identified at all as Amazon employees.
In my view, saying "I wish I were permitted to bring my values to my job doing UI design at Amazon" is not in any way speaking for the company.
If we as a society don't like it, we should enact laws for/against it. Though, I agree with another poster here that it is practically impossible to change any laws at this point. The whole system seems to almost be designed for snail-paced gridlock.
What do we think Amazon would/should do if someone external to Amazon went under an entity name such as "Amazon Executive Committee" and posted controversial/activist like content? I would imagine that Amazon would attempt to deal with the negative PR of some people thinking that this is some sort of official Amazon group.