I've never been good at situations like that either. I've gotten better but by no means an expert. If you are at a show sometimes reporting them to the higher ups will help (I had to do that when I saw someone duct taping their child's feet into the stirrups and I wasn't going to sit around and possibly watch a child die.)
Out on a trail ride there's really not much you can do other than confront them about it.(Which can cause a huge stir, which I avoid) Or what I usually do and strike up a conversation with said person and ask them their opinions on something based on the situation you feel uneasy about, without letting on it's about them. Turn it into a nice conversation and then give your opinion. Sometimes people don't know better and don't want to ask for help and by hearing someone else's opinion in a neutral "zone" (because I can't think of a better word) might give them an idea of they correct way to do things. By doing it the conversation way it's much less confrontational and might even make them think it was THEIR idea to try something different rather than someone else telling them what to do.
And then you have the people they are too far gone to help. Those are the ones that it's their way or the high way. UNfortunately not much you can do about them other than avoid them or report them to the proper people if you are really uncomfortable with what they're doing.
As for keeping cool during these situations. I usually keep composure and then once out of earshot I go on a ranting fit either to my horse or to a friend about it. =P