I'm going to out my best friend's cheating (now ex-) girlfriend in public
Why do you want to do that to his girlfriend?
I've heard rumors about her for years.
These matters are very private so it would be rude to address them in public. People will think you are immature.
Am I immature for bringing it up or is she immature for cheating?
This is something that should be handled privately. It could hurt your friend if you do it publicly.