You're right, it's definitely legal. The US has at-will employment, with some exceptions regarding discrimination, but political opinion or party affiliation are not protected classes.

This argument takes place entirely in the realm of should, rather than can. In this context, I meant "do they have to keep employing someone" by the standard of people arguing that they're wrong to cut ties over this stuff.

Like you, I assume there are things we don't know in the Carano case (that's one reason I criticized those who jumped to conclusions). But I have seen reporting that this was far from the first time her bosses were unhappy with her social media posts, and they had previously asked her to tone it down.