No matter what kind of video content you're watching, be it animated/live-action, you definitely have to subscribe to the idea of willing suspension of disbelief. Action shows have tons of bad guys that can't hit the hero with one shot, but the hero can take out enemies with just one bullet. Musicals have us believe that everyone can spontaneously bust into the same song and the lyrics are already common knowledge. You just have to sit back and enjoy the content.
While it's very hard to find anyone that says they aren't willing to put aside their issues when watching live action, some people find animation just too 'unreal' to follow along with. Again, this has a lot to do with animated features that take on serious tones rather than more traditional American cartoons. Seeing ducks and rabbits beat each other up isn't an issue, but watching two people try to solve a murder is just too far-fetched to subscribe to.
I don't know about you, but I actually find myself having an easier time believing what's going on in anime than I do in live-action shows. I can watch the content no matter what the medium, but an anime setting works wonders for me. Seeing real-life actors appear in multiple TV shows and movies kind of ruins the feature for me. If I see one actor play a big TV role for 5 years of his career and then pop up in a completely different movie, I have trouble separating the two. With anime, you never see that issue. It may come up through voicework, but I believe it to be much easier to deal with a similar voice than a same face.
The animated medium lets me complete escape into the story that is being told. I don't have to tie it to real-world actions or anything like. Especially when it comes to anime, we often deal with some truly serious issues that take place in absolutely fantastical settings. These amazing locations, be they based on real life or completely made up, paint a very specific picture in my mind. Then, when I am thinking about an anime at a later date, I actually tie those characters into the real world. Anime lets me take my imagination and work the amazing stories into real world fabric.
Perhaps that's why I react much stronger to anime than live action. Traditional movies with actors just don't resonate as well with me. I can watch and enjoy, and there are plenty of movies that I really love. With that said, there are anime characters that I connect with and will never, ever forget. When I think of the story of Death Note, I remember the actions as if they really happened in my life. I think that's further proof of just how moving these stories can be.
Either that, or I'm way off the spectrum with this one. It's definitely possible that I'm a little bit wacky!