Make different words then rather than co-opting a word which already means something else.
There are easily 30 different genres represented in anime, so it's not a "genre" word. D'ya mean sports animes, action animes, fantasy animes, mecha animes, historical animes, romance/drama animes, romantic comedy animes (and if that, d'ya mean harem comedies or do you means shoujo romcoms), d'ya mean idol animes, or d'ya mean school slice of life. Or perhaps more general slice of life (Aria), or philosophical animes (Mushishi). Maybe you want one set in the gangster era that's a black comedy (Baccano) or one that's a tragedy (91 days). And you know that's only scratching the surface of possible genres you're going to find.
Clearly "anime" by itself is useless to define a "genre". Many people watch anime because they want 2D animation with a wide range of genres. And nobody else is offering that. It's like if every shoe shop sold one type of shoe each, and then you found a shoe shop with 40 varieties of shoes, you'd probably keep going back to that shop to find new types of shoes even if there was some technically better shoes at one of the little shops.
For "style" many people also watch anime because they like the language / watch subs, and there are many cultural idiosyncracies included. It's a mistake to think than in an animation which is a story with visuals, music, dialogue, production, etc, that "style" can be just boiled down to what shape people's heads are. boondocks is a cartoon where the characters have "anime shaped heads". This in no way means it completely encompasses "anime style" in a way that you couldn't tell the difference.