A naive, uneducated, and often misinformed fear of people who identify as 'Furries' (and others who identify as Pansexuals), rooted in personal insecurity. Most often, individuals expressing Furry Worry have a traditional and even archaic world view that would come crashing down were they to accept the lifestyle choices of Furries; yet, in truth, their fears are rooted in a suppressed belief that they themselves would get a kick (if not a kink) out of being a Furry.
Jack was freaking out with Furry Worry during DragonCon, but we all know that if he put on a Furry suit he would totally get off on it.