If a brony doesn't like MLP for the fact that the characters are anthropomorphic, then that would just make them a freak that fantasizes about being a poorly drawn cartoon that is adored by tiny little prepubescent girls. However if you do enjoy them for their antho qualities, than your a furry.
Depends on how you define furry, I suppose. For instance, I've never identified as a furry, I do however call myself a brony solely by virtue of, I watch the show, I read the comic, I have some of the toys and I occasionally browse EQD for cool pony stuff. That is the extent of my involvement in the fandom, I guess you could say I'm a moderate fan because I don't hang around on forums, draw ponies, attend cons or write pony fan-fic or anything like that.
Now, as for being a furry. Some people go as far as to say, if you like anthropomorphic animal characters, you're a furry. This is a hard one for me to believe, an absolutely massive percentage of animated characters, be they from cartoons/movies/games, are in some way anthropomorphic animals. I love the Star Fox games, does that make me a furry? No, I don't think it does.
Again though, there is this vagueness of what defines a Brony and what defines a furry. To me a brony is an adult fan of MLP, simple as that. To others it only describes very intense or hardcore fans, or active members of the community, hell some people exclusively use it to describe cloppers. So this creates a kind of disconnect which really renders your statement impossible to prove because these are two terms with very loose definitions to begin with. Also it's just really fucking stupid.
Do you even know the definition of a furry or did you just make this without looking it up? I don't care if your a brony or not. Everybody should see that this is bullshit. Even if what the stamp says is wrong, it would not even be an insult if it were true! Sorry. Sometimes the stupidity of the internet gets to me.
Umm... Aren't furries people who like to draw anthro animals? Ponies are not anthro unless they are drawn that way. There is such thing as a person who is both brony and furry, but being brony=/=Furry. They are similar, but not the same. Like bats and birds. Both fly, not same species.