I don't hate furries, and in the broad sense, I don't think most so-called furry-haters (even self-proclaimed ones) hate furries, either. Let me draw you an example. A lot of this will probably come off as irrelevant autobiographical spew, but bear with it, and I think you'll get the perspective.
I recently moved to Milwaukee with my girlfriend -- Bay View specifically. You could probably call it the San Francisco of the midwest; there are a lot, a lot, a lot of gays here. I've made lots of gay friends, and am even comfortable with them playfully hitting on me, despite my straightness -- after all, they're dudes, just like me. They just happen to like men, and I take their flirting just like the playful flirts I'd toss at a cute girl, even if I had no interest in her as a partner.
I also go to a few cons each yeah, but my favorite of all of them is Penguicon, usually held near Detroit (far enough outside, of course, to avoid the Detroit squalor). Born from the roots of a Linux enthusiasts' convention, it's blossomed into an all-encompassing geekfest, with interests represented across the board. This includes furries and such, and while there I have even made friends with a fur-suiter.
Thing is, I am exactly one of those anti-furries you lament. Here's how it is:
These friends of mine are not flamboyant. If you see a gay in the street, wearing neon orange plastic suspenders, a neon green thong, some funny glasses (also neon), and nothing else (unless you count the chest hair), that's funny, and it deserves to be laughed at - and if he keeps a good sense of humour about it, that person is awesome, and an excellent representative of his community. If he gets in your shit for laughing at him, though (again, not for his homosexuality, but for his ridiculous public display), and then calls you a homophobic bigot, then he's a tool.
For the one fur-suiter I have met (and in real life, that's a 100% sample set for me), has been cool. A large part of that was likely that he was also a mascot - he has taken his fetish and turned it into something else, legitimate. It's a brand, and he uses the brand to sell merch. Good on him. He's not a typical suiter, though. His suit says, "I sell things," not "I really want to remind you every time you look at me that I fantasize about fucking animals."
This is the distinction. Most people don't really hate furries. A simple, "I am a furry" isn't what draws the hatred. The cries of persecution after a few weaksauce pseudo-insults turns it from 'whimsy' to 'nuisance,' and that's where the hate comes out.