The following is based on comprehensive, archived research regarding the interactions between furries and bronies:
According to Fred Patten and other fandom historians, furries once known as fuzzies were fans of "serious funny animals". While funny animals were often highly anthropomorphic at the time, anthropomorphism was not often presumed until AnthroCon etc implied it. The idea of serious funny animals was referenced first apparently in Kimba the White Lion which was as about anthropomorphic as MLP albeit proto-fandom and the idea behind Kimba expressed the characters as unique and human-like intelligent among the rest of the animal kingdom. Believe it or not, the first "anime" largely contained funny animals, serious funny animals in Japan is now known as "kemono". The origin of "fuzzy" is thought to date to the mid 70s and is not a reference to H Beam Piper's works but rather as an esoteric funny animal APA term though animal-like aliens was one of sci-fi fandom's greatest attractor to the furry fandom which facilitated grounds for "serious funny animals" in sci-fi situations (i.e. Albedo Anthropomorphics and Thundercats). Funny animal fans would have been regarded as "funnies", the postfix trend possibly originating from "Trekkies", etc.
Though the term "furry" would commit moreso to those who socialise with other furries and aren't just a part of the furry fandom but its derivate community.
The sci-fi fandom in the late 70s would also describe furries/fuzzies during the early fandom as "intelligent animal characters", as in animals with a human-like intellect, there's no mention of the word "anthropomorphism" though the facial features were most often with a very human-like expression in the toons. Steve Gallacci and Stan Sakai lead the succession of the use "anthropomorphic animal" in the early 80s.
Though I'm sure MLP would come under furrydom in the classic sense. I think the modern furry identity has been collapsing moreso into two definitions "anthro animals" and "fans of cute animal characters", neither is wrong, there's no police or fandom core, only people and landmark conventions, etc. It's the fact that furries are so loosely knit that leaves them open to scrutiny when a smaller portion of it gives a bad name to a greater part. Brony, itself, originated on the (relatively furry-dominated) /co/ forum of a very controversial website known as 4chan. Certainly, however, furry fan groups discussed MLP before MLP:FiM and also thought well about the pre-release of FiM, many furries became bronies and formed perhaps the greatest amount of its base originally. The larger parts of furrydom is concerned with art and belonging, away from reality around it, digital artists and fursuiters form it mostly. Though, there is certainly a borderline plutocratic-like (largely subconscious) element to the furry fandom known as the "popufur culture" which demands a great identity, art skills and a furry lifestyle. In hunger for fandom actualisation, many furs have tried to gain popularity in the fandom by means considered illicit and ridiculous by the general public, which lead to a certain episode of CSI. Sadly, the popufur obsession has given much drama and bad name to the community that furries tried to make other sites free of it (since dA and FA condoned it), such as Weasyl which was created in reaction to FA's apparently narcissistic merge with Furocity and the destruction of Artspots.
Because of all this drama, reasonably, many bronies rejected furries purely due to the stereotypes and issues, in reaction to bronies, FA etc even attempted to ban MLP artwork but this lead to concern that the Sonic artists should have to be banned but there was too many against this ridiculous control attempt that FA has been rendered infamous for. For popufur culture, dA even relaxed its maturity levels in a deliberate attempt to get money from those temporarily leaving FA, much to dA community's shock as it forced innocent artists to compete with the selling point of the more mature ones.
Doubley so, bronies made their first con and migration to tumblr at the time in protest to dA and the furry community.
Moral of this post: The Internet never forgets what you put on it, less so even its users. Fandom history was made, but many bronies and furries fought each other once out of propaganda and misunderstanding.
Big hug?