It's a good reminder, and I can see how some posts would be a red flag to coaches, gym owners, team parents, etc. if a parent, gymnast, or coach was posting lots of bad things or misinformation about a program or particular individual with a significant amount of identifying information. I also think it's good to err on the side of caution for safety purposes, gymnastics is a small world.
I think it's silly to throw members out of a gym based on frustrations vented by parents, coaches and gym owners are human, it's natural for them to make mistakes or act in a way that causes some frustrations among parents. While it can be hurtful to realize someone is upset with your actions, it can also provide something to think about. If a gymnast of mine or her parents were posting on here and I figured it out, I would try to use their posts to help me as much as possible. Perhaps realize how my actions were being perceived by others and make necessary changes in the gym. Parents and gymnasts also post plenty of great things about gyms and coaches. I don't get a whole lot of feedback from parents and athletes, so I love having a place where parents and athletes voice their complaints, concerns, and things they really like as a means of self growth as a coach. I might not agree with anything, and some things might seem offensive, but such is the nature of any profession where you are providing a service to people and being payed for the quality of that service.
It would be a different story if people were posting outright lies that could greatly affect a coach or gym (false allegations of abuse, misuse of funds, etc., but I don't think that is often the case here).