Yeah I'm really tempted to have this take, because it is really stupid that any news outlet is getting multiple days of content out of a stupid tweet with negligible harm to a patient. This does not need to be covered by the national media, but--with the caveat that I am specifically commenting on the source of the story linked in the OP, and discussing the source has to be fair game when discussing a story, and I'm not saying anything positive or negative about their competitors--this is Fox's schtick, where they find a single anecdote and they blow it up into proving their worldview that the woke radical left is full of callous jerks who are out to get you.
But at the end of the day, that is sort of the point. This is exactly the kind of thing that can happen to you when you let your personal views impact the care you provide patients, and then compound that mistake by taking to Twitter and sending such an ill-advised tweet. Once it's out there in the world of social media, it can spiral exactly like this and there is nothing you can do to take it back. Physicians are, and should be, held to a higher standard. So while it will truly be a shame if her career is ruined over a couple of really, really poor decisions, it would also ultimately be no one's fault but her own.