Well, to be quite honest, I don't think it has to with "being different." I think it has to do with a small cluster of the unrealistic and "colorful" characters (or "sparkledogs and glittercats" as you called them) disdainfully referred to as "Neons."
Whether their colors coordinate, or not, neon colored characters tend to hurt the eyes of the player looking at them. Let me ask you this, why would most people rather write with a pen or pencil instead of a highlighter marker? Because it's clearer and easier on the eyes to read pen and pencil writing than strain with the bright colors of a highlighter, much like a neon critter.
Now I personally have a vast amount of unrealistic colored characters however, the mass majority of them would not class as "neon" and if they did, it would only be a portion of their design. That's just my personal preference. However, I have no issues with roleplaying with someone who has a vibrantly colored character but they will have to understand if it starts bothering my eyes the RP will either have to end or they may have to temporarily adjust the tones to be a little darker and less "in your face".
In another thread I explained my dislike for rejection from RP's based on an unrealistic appearance (although that was more about subtle things rather than your typical bright green "sparkledog") but I would not make the request of someone to adjust their character's looks unless the looks of them really does start to make my eyes physically hurt.
But there is also the general trend online for hating "sparkledogs" and "glittercats" and I think it very much exists in the real world too. I guess it stems from the idea that animals must be depicted as realistically as possible or else if they're not then they are classed as "for children." [How "werewolves and "dragons" earned a free pass from this, I will never understand] That just seems to be the general opinion of most people I know, because most of them will automatically class anyone depicting anything with an animal that is unrealistic as for children, silly, or "furry" type stuff. I am not a furry, but I do know that group of people does tend to receive a lot of hate because of a small portion of them (though not all) is thought to do things I won't mention on a family friendly forum, if you catch my drift.
Though if we are all playing on a game where the main characters are animals, that kind of hate is less grounded because the people who hate furries that much would more likely than not, NOT be found playing this game. So I really think it does just come down to the fact looking at such bright colors for too long can hurt people's eyes and they would rather avoid it or that some people have the perception that it is "immature" and "child like" somehow. Still, it gives them no right to treat you rudely out of character.