That's a bit different. How do I communicate this effectively? It comes down to hobby vs fandom vs subculture.
Using the closest to universal definition available, a hobby is a repeating action not average for the culture by its own nature or by extent. A fandom is loosely associated individuals bound by their enjoyment of a particular thing, typically consisting of multiple hobbies. A subculture is an autonomous collection of fandoms, which contain hobbies.
Most anime and comic cons loosely be defined as "cartoon fans," as most anime fans also enjoy western cartoons and vise-versa. The nature of these fandoms is derivative of media that both typically partake in. I should say that the two major subcultures - anime and comic - are very compatible and overlap a lot. Western cartoons are not anime or comics, but often the individuals are one in the same. By this I mean that the hobbies contained in both subcultures are nearly identical - cosplay, fanfiction, fanart, etc. Even if the fandoms don't line up, the hobbies do. That allows the subcultures to mesh well. More lines up than does not.
Furries are not a fandom, they are a subculture. The majority of the fandoms are self derivative. The hobby expressions - fursuiting, art, RP, writing, dance, puppetry, etc - only line up in a marginal sense. The treatment of the costuming is also markedly different - fursuiters are closer to larpers in that they are acting - versus the more glamor or photo -oriented cosplay.
The reason furries do not belong at anime cons is because the hobbies do not line up nearly as much with as many people. The shared hobbies - art and costuming, are only superficially similar. One is representational and derivative; costumes emulate, art reproduces an icon - the other is autonomous; art produces individual likenesses, costumes are a medium for acting. A pokemon fursuiter and a Gijinka cosplayer do not enjoy their hobbies the same way.
Beyond tl;dr, I know.