People should not be fired from their jobs for one error of judgement unrelated to the performance of that job, or for not adhering to whatever the popular opinion/values of the time happens to be. It reeks of fascism any way you put it.
I think a suspension, which I believe is what they’ve done, is appropriate. She should be punished but not with termination.
If you work for SNL, that makes you a public figure, and you are responsible for what you put out in the public with your name on it.
That sounds reasonable enough to me.