Yes.
> She posted a joke on Twitter mocking the idea that white people couldn't get AIDS.
Even if you believe the subsequent backtracking, that's still a profoundly stupid thing to be doing in that circumstance, and it shows a complete lack of any critical thought as to how your actions and words are perceived.
Of course I believe the subsequent backtracking. Have you read the New York Times article? Most people aren't racists.
> ... a complete lack of critical thought as to how your actions and words are perceived.
A lot of people have times when they don't think about how their words will be perceived. I sure have, and I'm sure you have too. However, I do not believe such minor stupidity should result in immediate loss of job, without warning.
You're being somewhat generous here.