Well before I say anytging, can you give me the definition of a furry? (I watch anime, draw chibis and things like that but Ive never understood what a furry is!)

What I do in this scenario is treat the anthropomorphic folk like any other fantasy race. Don't make the story pay too much attention to it. Just kinda mention what they look like in passing. Since you've got other things like elves and orcs and all those classic things, they shouldn't feel out of place.
Of course, the number one thing to do is not worry about looking like a furry. The more you feel the need to remind the audience that you aren't a furry, the more it'll look like you are. Just roll with the story.

I spent four years trying to get this down well enough to finally feel comfortable writing the story that I am now.

Just so you know, I cant read comments not made on the 3DS system...idk if this would work but you could make something like this picture and post it, then tag me in it and ill see it and comment my help! ^.^

Many people know what those are (especially lycanthropes) and I figure as long as you have the human-like races in there, they'll just figure the anthros to be just another race, not furries.