I wouldn't say they are related.
Furries just took ponies and ruined them with their NSFW art. There was a time where I went onto good images, looking for a picture of Big Mac to put as a wallpaper on my laptop and I saw like a load of anthro Big Macs some had drawn in a NSFW manner.
I don't hate furries per se. But they do seem to try and convert everyone they come across (The ones I met anyway. There is a dude at university who is one, who keeps trying to force it on people). Bronies, just seem to be all laid back and casual.