I think this is a real tough one to answer, since there are so many variations. The biggest problem I see with it is the natural human tendency to stereotype others who do not fit into a particular person's own frame of reference. It is very hard to fight a stereotype, and it is very hard to define a type of person who does not fit one, if you know what I mean. Responsible gun owners are found across the entire spectrum of political views, religious views, race, age, gender, etc. The big point of commonality is the ownership of guns.
It is easy to assume that people who think like I do about guns think like I do about everything else, especially since I am right about everything else as well as guns.
Now, for you sensitive types reading along here, that last sentence was a joke! But behind the humor is a very natural human assumption. When we find a point of commonality, it is very easy to assign other points that may or may not be true. It is very hard to reconcile differences once we find those points, and when we do find them, we usually react adversely with some sort of illogical reaction.
I am not saying
everyone acts like this, I am only saying that these are natural human tendencies. I think the best thing we can do when we encounter an anti-gun person is to make them think. Show them that you are not a wild eyed lunatic driving around drinking and shooting up the town every Saturday night. At the very least they will stop bothering you about your use and ownership of guns. I think the biggest problem with anti-gun people is the tendency to assign human characteristics to inanimate objects. "Guns kill people" is the thing we hear so often. Well yeah, but so do knives, clubs, cars, swimming pools, etc. But how many bad guys lurk around pools waiting to throw someone in? If we had no guns, people would use knives, since it is the evil nature of the human heart which kills, not the inanimate object which was used to do the deed. But try to get people to go along with that!
I have often found that people seem to think that there is something wrong with me because I own and carry a gun, but in reality, the problem is with them, not me, and there is not much I can do about that. While we can influence others, we can only change ourselves.