Perhaps the most effective way to dissolve defense mechanisms is by providing corrective experience. Corrective experiences are experiences that allow a person to learn that his ideas are incorrect in a safe and non-threatening way. To provide a corrective experience, you first allow the person to attempt to project his or her incorrect ideas onto you. Then you demonstrate that he or she is wrong by your behavior, not by arguing.
For example, the anti-violence person may unconsciously attempt to provoke you by treating you as if you are an uneducated "redneck." If you get angry and respond by calling him a "stupid, liberal, socialist," you will prove his or her point. However, if you casually talk about your M.B.A. and your trip to the Shakespeare festival, you will provide the person with the opportunity to correct his or her misconceptions.
If you have used the above techniques, then you have already provided one corrective experience. You have demonstrated to the anti-violence person that martial artists are not abusive, scary, dangerous, sub-human monsters, but normal, everyday people who care about their families, friends, and even strangers.