I wouldn't let other people "move" you like that. Ask God for His peace and that only He can "move" you. After asking God that, my heart has been so still so that no one phases me when being name-called from the Bible (which no one is suppose to do anyway). If our heart is not "moved" by others, then we can concentrate ever more on His message in love to those who do/say such things.
You also have to keep in mind (as do I at times) that they just don't know what it is they are doing or saying. It's just as Jesus and Stephen has said: Then Jesus said, "Father forgive them, for they do not know what they do." Luke 23:34
They were stoning Stephen as he called out: “Lord Jesus, receive my spirit!” Then he knelt down and cried out with a loud voice, “Lord, do not charge them with this sin!” And saying this, he fell asleep. Acts 7:59-60