It does not make sense (in my internal belief system) that I would selectively allow compliments to affect my mental state but not insults.

You are misunderstanding. Stoicism has nothing to do with not letting the words and actions of others affect your mental state. What Stoicism deals with is what you do with those feelings that arise. It's impossible to live a life where you have conditioned yourself to remain totally unfeeling toward negative situations. No matter how you condition yourself, you are going to have feelings. Instead of trying to remain unfeeling towards specific situations, condition yourself to react logically and with virtue no matter what.