Maybe it is because the holidays brings out the best in us all, but I have seen a lot of people talking about how do deal with negative people AKA trolls on social media.
I would suggest taking the approach that many universities have which is to make a social media response guide. The first one was developed by the Air Force academy but many others have followed suit. Here are a few good examples
But I think it is best to have a discussion in advance and come up with your own plan as to how to deal with trolls based on your campus culture. In the end you have to address each comment as a unique situation.