You’re mixing two separate questions. One is whether your boss has the freedom to hire and fire as they see fit, where the answer is yes except for certain protected classes. Their money, their rules…
If he’d sent out a memo saying any management initiative was wrong and they were stupid he could be fired for it in the state of California. He just wouldn’t have been able to turn it into cash from right wing causes.
The second question is whether this is science being squashed as his more emotional supporters frequently claim. I don’t think there’s any reason to conclude that since this was a really lousy attempt at scientific analysis remiscent of the creationists who try to sound science-y but are ideologically prevented from actually practicing science.
Management decisions don't come with references to scientific papers, or any claim that they are backed by science. Damore's memo, on the other hand, did exactly that.