I always find it weird that people talk about furries and bronies as two completely diffirent things. I mean, I can understand why, but the characters in mlp ARE anthropromorphic ponies.
When it is all said and done, at the end of the day it is if you choose to have that named labeled on you or not. I consider them both the same thing, but some people find that offensive. The meaning of being a furry has become skewed over the years. My guess is people do not want the stereotypes that come with being called a furry. The thing is you can't escape stereotypes and pretty much what happened to furries a couple of years backs is literally just happening to them right now.
The way I see it though whether you choose to have the name or not, both groups should understand how society treats their group and should be more understanding to each other. I also feel we both should stand up for each other when people talk stuff about one of these groups. I have read about ponies that literally hate furries and furries that hate bronies. I know at my job one of my co-workers was talking bad about them, and I had to explain to him just because it wasn't normal to him doesn't mean they don't have a right to watch the TV. I also explained it was their life and they can watch whatever they want.