I tell myself quietly at night that I am not a furry... but then Kemono Friends comes along and laughs smugly.
Kemono Friends follows the line where animal features are little more than accessories. Like hair bands, bracelets, and skirts. Ears, tails, wings aren't enough for a character to be a furry. Often times there's an amusing personality quirk that alludes to the idiosyncacies of the animal in question.
By extension, most monster girls aren't furries either. Monster girls tend to be rooted in mythology. In myths, most of the time monsters were evil and exist to be slain by human heroes. When they weren't evil they were affiliated with some kind of god or divinity.
In modern times, lonely gamers were tired of fighting and killing sexy lamia mobs. Even when the MO of these monsters was literally seduce, rape, kill the dream of taming them with the hero's dick endured. And so the monster girl fetish was eventually born. And as a practical matter, monster girls are just more heavily accessorized than most.
What's known and rightly despised as furries come from a completely different sub culture where unimaginative and depraved people role play as beasts. These degenerates coopt characters from other and completely unrelated franchises for their own amusement, threatening to ruin them.