I think I'm a little late.
I don't like anime too. I came across many great games but I didn't even think about playing them because they were anime. Expressions are like, alien, with giant eyes and stuff. Characters are not close to being original. Every character pretty much looks the same. You know, stupid hair, strange colored eyes, shape of the face and things like that. I'm not a big fan of western animations too but at least they had varied characters. I really understand you OP. I have an urge to scream when I'm surrounded by anime fanboys. Still, it's not as bad as being surrounded by Twilight fanboys.
"Western animation" is big. A crapload of different cultures and countries are doing it and that's why it seems varied. Anime is based on one culture and we got a lot of it. Quantity of anime is really getting the quality of anime down.
I'm very late to this necroed topic, but this is largely how I feel. I haven't let my distaste for anime prevent me from playing a game that was anime themed, but it does detract from the enjoyability of it sometimes. I'm sure there are games that are so strongly filled with anime tropes that I wouldn't play them, but I probably wouldn't like them for other reasons.
That's really it: I just hate anime tropes. Because I'm not accustomed to them, whenever I see anime all I can really see is the tropes jumping out at me. That in turn makes it feel like all anime is the same, even though I know it's not.
Other than the tropes, a disproportionately large amount of anime that I've seen any significant amount of is filled with things that are just downright strange and offputting. I can't think of any specifics, but the fascination of putting Japanese demons in anime probably has a lot to do with this.
I really can't watch anime that doesn't try to be more or less "normal". Something like Gundam Wing, for lack of a better example. The wacky expressions and freaky supernatural stuff aren't getting in the way of watching it for me.