If you don't try to prevent your community from doing something bad, you're morally responsible for the outcome (perhaps legally responsible too).
It might be fun to join the Amy Baking Co fan page and watch the increasingly furious, aggressive, messages. It might be fun to let your members relentlessly hound someone they (and you) dislike.
Yet actions have consequences. You can't predict what happens when your members hound an increasingly unstable person. Especially one whose business and reputation has been publicly destroyed.
History suggests this has the potential for tragedy. It's the potential for that tragedy which should prompt you to action.
There are many grey areas in moral responsibilities for community actions. This isn't one of them. Online bullying is real. It has proven, fatal, consequences. No-one, especially not the members doing the bullying, wants that outcome. Be sure to tell your members that.
...and this goes for our fellow community professionals too.