That would depend on where the parent is from. In Germany you would absolutely have a case if your public University tried to make you use Facebook. In fact, you could probably skip the lawsuit and just report it to the appropriate authority.
I don't think any public university is making someone use Facebook. The issue is that every single event is posted on Facebook so your options are either 1. create a Facebook so you can find out, 2. don't participate, or 3. inconvenience your friends by asking them to tell you about all the events.