Grave of the Fireflies is commonly referenced when discussing things even more cynical than Eva; indeed, it is so disturbing, many who have seen it insist that they would never be able to watch it again. Ironically, it was made by Studio Ghibli, well-known for their idealistic productions.
The 2007 Beowulf paints the title character as a Bad AssAnti-Hero, which ironically puts the movie at the opposite end of the scale from the original Old English poem (which portrays him as an honorable hero who does not, for instance, take advantage of the noblewomen he encounters). Being a self-aggrandizing braggart was part of the ideal heroic package in those days. The film plays this up and depicts this as it would be received today.
WALL•E. Just because it's After the End doesn't mean it's not the very definition of idealism. The Power of Love and humanity remembering what made it great are all that's needed to reverse an ecological Armageddon. We're oversimplifying here, obviously — the movie is fantastic — but seriously, it pegs the needle so hard onto the Idealism side that it's a surprise the meter doesn't break.
Disney's Fantasia, as far as it has a position, is generally closer to the idealistic end. Even the Night on Bald Mountain segment ends with Chernobog repelled and returning to slumber. Bruno Bozzetto's response, Allegro Non Troppo, is far more cynical.
Batman: Mask of the Phantasm is blisteringly cynical for a kids superhero cartoon. (The major theme is that Batman's life always takes a turn for the worst and that he is damned to sadness and loneliness)