I strongly doubt firing people for making stupid jokes is going to cure these problems. You may make people more careful of what they say and do in public, but the false beliefs will still be there. If doctors believe black people feel less pain, that’s something to handle in med school.
I make a pretty strong separation between racism with real world consequences, like those people you read about who call the cops on a black man because a black man can’t own a nice car honestly, and, shall we say, cultural insensitivity. Actions that obviously insult people due to their historical context, but in themselves are not harmful. Firing a nurse for something like the former might be justified, and the kind of behavior described in your second story definitely should have consequences for the involved because that involved their actual work as physicians.
Now, that really isn’t a good parallel. Getting a swastika tattoo indicates a firm commitment to a violent and genocidal ideology, and if he changed his opinion he’d make sure to remove it. It’s not comparable to dressing up in a way that you find offensive.