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.