I grew up in the Deep South, and you can really change the way people feel by being unflinchingly friendly. People who hold controversial opinions generally know that they do (if they aren't crazy) and expect people to recoil at first contact. When you don't recoil, it throws them and makes them think. At that point, you are entering mind-changing territory. Then you start asking them questions that allows them to do 80% of the talking. They will usually stumble on their own logical fallacies at that point, and you have thus led the horse to water, which is about all you can do.

Not very many people are very good at this. Which is unfortunate.

TL;DR When you get all worked up over the way people are talking, you have allowed them to seize control of the debate and have generally lost the opportunity to change that particular mind.