Hugely nerdy rant incoming:
I'm getting really annoyed at the constant question of, "Are bronies furries?" The answer is: They are if they want to be. Yet I see lots of folks who try to argue that bronies can't 'qualify' as furries for various reasons.
The base definition of furry is, "a person who is a fan of media containing anthropomorphic animal characters". That is the one characteristic that every furry will have in common - and so it is the only definition by which one can fairly define the fandom. When you start tacking on things like, "Furries have a fursona to whom they feel a deep personal connection," you're delving into a No True Scotsman fallacy. Likewise, when you start saying things like, "They're only fans of one show," you're adding on a specification that would qualify some people who definitely ARE furries.
Given this basic definition, we can determine whether a fan of My Little Pony qualifies as a furry:
The show contains ponies, dragons, donkeys, cows, horses, zebras, dogs, etc. (animals) that, while being primarily quadrupedal, have human-level intelligence and social interaction. This falls under the definition of anthropomorphism - the attribution of human physical or mental characteristics to a non-human entity.
That means that a brony - a fan of My Little Pony: Friendship is Magic - is a fan of media that contains anthropomorphic animal characters.
Does that make them a furry?
Nope. That label only applies IF the individual chooses to apply it to himself or herself. It DOES mean that if the individual chooses to take that label up, that they are 'justified' in doing so and fit the definition of that label.
For a fandom that consists of people who portray numerous different species (and therefore should be MORE accepting rather than LESS) and who are, on the whole, ostracized and frequently mocked by the mainstream culture, to have so many people who fervently try to segregate and disqualify through irrational rationalizations really pisses me off at times.