You can get fired for saying many things, there is not freedom of speech there. It is part of cancel culture, but legally speaking if enough pressure gets put on your employer for something you say, you can be fired.
I disagree with Robbie Soave there: it can still be considered a "freedom of speech" issue, it's just not a First Amendment issue. But this is America: we're cool with giving business power over individuals we don't give to the government. A philosopher makes the case here, with rebuttals from others who don't buy her argument.
Can we at least agree JK was not cancelled? Some people collectively decided they now deem her an asshole, but both her wealth and the cultural impact (world-wide) of the Potterverse essentially makes her an uncancellable individual. My opinion on the discussion at the heart of this isn't really relevant (seems like something that should be resolved between Cis- and trans-women). More generally speaking, I do think both sides are guilty of oversimplifying issues of what are essentially competing rights between two historically disenfranchised groups. Any simple solution to such complex realities must almost always be bullshit.