There's a huge gulf between dictating the religious beliefs or political views of players and employees and endorsing them (or staying silent about them).

Dictating anyone's thoughts as opposed to their actions is a highly dubious proposition at best.

But it completely doesn't follow that you can't criticize them. University professors say weird stuff now and then, and for the most part the university administration says, "University U does not endorse Professor P's <highly-questionable-at-best statement>. Although we stand by the freedom of speech of all our faculty, we find P's statement <bad>; our values are <positive statement>."

So you're setting up a false dichotomy here.

Of course, there's nothing terribly wrong with an employer saying that certain jobs involve presenting a public persona of a certain type, and if the individual can't do it, they aren't fit for the job. They can think what they want, but as perpetual representative of the brand, they have to always keep it to themselves. But it's best to set this kind of thing up in advance, not go, "Oh wow, we don't like what they said. Nail them!"

Even with at-will employment, that's pretty slimy. Make the conditions of employment clear, and everyone is at least warned.