Put simply? We were raised on it. It may seem idiotic and shallow, but our snap impression of many things that we're raised on as kids, particularly as we get older, is to not take them seriously. After all, WE thought it was good when we were like....ten. This effect is only amplified when you invariably get bored or sleep-deprived or medicated or injured enough to look up those nostalgic little gems from your past and realize how utterly awful things like the plot and dialogue and catchphrases are. I think all of us can remember a few cringe-worthy 90s or 80s cartoon catchphrases off the top of our heads.
Speaking as a massive geek for a moment, this is seen alot by fans of Tokutatsu like myself. The thought that there's something actually entertaining to a person that's over the age of 12 hidden in the source-material for the original Mighty Morphin' Power Rangers is impossible to most people. Even if you get people to give it a shot, the method of Live Action invariably invokes nostaliga, and the suspension of disbelief shreds faster than wet toilet-paper. Nothing wrong with it, really. People just like what they like, and not everything targeted towards the realm of children and young adult entertainment is well-written and charming enough to allow older kids and adults to enjoy it too. Some of it really is just that bad.
All that said, Eastern Animation brings something different to the table. Aside from the obvious difference in art-style and details, it's also just plain old different. and as adults, there's just a different feeling between watching say, Spongebob, and watching something like Naruto or Bleach. At it's core, I'd imagine it's mostly that the guilty pleasure effect is minimized.
The Disney works are really in a league of their own, though. They're truly family films, but ultimately they still likely suffer from the same issues, although likely to a much lesser degree.
Suffice it to say, the ability to watch Adventure Time just as easily as one might watch Hellsing or Evangelion, is just a matter of perception. Not just how other people look at the works, but also how the viewer sees it as well.