I somehow like the art style in anime. What I should however note is that the reputation of anime is a bit colored by the typical over-the-top kind of anime which even for a cartoon is a bit well, awkward. And sometimes cool heroes are too cool etc.
However, anime is a very broad phenomenon. I've seen a few fragments on an anime taking place in European history and despite the art style being an attempt to give a proper image of how things went in Europe centuries ago. The fact that I immediately recognized the French army uniforms from the time of Napoleon Bonaparte, shows that the animators did do their homework well. Now I didn't see the entire work, but I've been told that even though the story is fictional the culture references and many aspects of the war back then were historically correct. Well, I don't mind to get my history lessons in anime style. I personally opt for content, and I'm really wondering about the entire work.
I've also heard that there are also anime stories in which a dead body is found and the famous inspector <your name here> comes to solve the case, and that when the killer is unmasked and the inspector telling the viewer how he could unmask the killer that you want to kill yourself for being so stupid to not see it for yourself as it was, just like in western works, so obvious that you simply ignore that. If you love those stories with real actors, would an anime style detective story be so bad.
And there's also hentai of course, the porn version of anime, where both the over-the-top kind of sex as the more softer style of sex can be found in. Well, I don't need to go into details.
Nearly all genres represented in stuff with real actors or other kinds of cartoons can be found in anime variants. Some of them good, and some of them bad, well just like real actor movies. Sometimes I can see though that the animates cheated a little to prevent them from having to draw too much, which removes a bit of a natural feel, like you see in early Disney classics, but then again, South Park is even worse in that, and once you got yourself into a South Park story, you don't mind that any more. Well, anime is in the same boat for me.
I have neither a true love nor hate towards anime. The art style is nice somehow, but for the rest, I do not like something just because it's anime nor do I hate something just because it's anime. If the story is good, the presentation is worked out well, and the actors did their job well... well...