Well, first if I can, I segway the conversation so that we are talking about fandoms or something of the like. I then say that a lot of fandoms are taken the wrong way, and then explain the issue of furs and media, but making sure to give them lots of info as to what a furry really is. Most likly they will respond with "Why do you know so much about furries?", then I reply with "Takes one to know one..." and then either they go screaming into the night, or except it. As long as you explain stuff first, then they won't be caught up with "awh mah gah, dis dudes a furry, this means he is exactly like this, and likes *censored for the sake of the forum*...
I really think that that is the best approach; Explain first so they don't go into shock and then stop listening
What is your favorite flavor/brand of gum?