If you're an at-will employee, as the vast majority of us are, companies can terminate your employment for (almost) any reason or no reason at all, and doing something that the company believes publicly reflects badly on it is definitely a reason. My company reminds us all the time, as I'm sure most companies do, to be careful about what we post on social media. People want to treat this as some kind of attack on free expression, but if you work for a private company, the threat that you will be fired for what you post on social media lingers over you constantly. Gina Carano, of course, was not an at-will employee, as an actress she would have had a contract, so her termination means one of a) her actions violated the terms of the contract; b) her actions did not violate the terms of the contract, but Disney was so bothered that they took her off the show even though they're still obliged to pay her (in which case, tiniest violin in the world for the rich person getting paid not to work); or c) Disney declined to renew her expired contract (which of these scenarios it was has probably been publicly reported, but I won't bother to look it up because all roads lead to "I don't care").
A few years ago, that lady who was not wealthy or famous also lost her job
that she probably actually needed, unlike Gina Carano, because she flipped off Trump's motorcade and a White House photographer got a picture of it that went viral (actually, she was specifically fired for reposting this already well-publicized photo to her own facebook account, apparently in violation of her company's social media policy against posting "obscenity" -- this could arguably be considered a pretextual firing if she had been otherwise protected from termination, but alas, she was not, just like most of us). So this does, in fact, cut both ways, the mean ol' liberals do lose their jobs over this too.
I guess if you want to have a conversation about all the ways in which we have ceded way too much power to corporations and we fail to adequately protect workers, that would be a good conversation that we should have (in this thread, or like, as a whole society), but if you just want to stand in solidarity with a rich and famous person who lost this one job but will experience no hardship from it because she is, after all, rich and famous, then, well, who cares. This, like most culture war issues that raise hackles on the right, doesn't matter.