Not only are the adults in this poem against the young lovers, it turns out that heaven and hell are lining up against them too. At least that's the speaker's theory. He never quite comes out and accuses God of taking away his girlfriend, but that seems like where he's headed. It's not exactly a religious deal, he just seems like a paranoid guy who thinks the whole universe, even the parts he can't see, is ganging up against him. When tragedy strikes, it's not uncommon for people to ask big angry questions about heaven and earth.
Although the poem emphasizes the intensity of the love story, it places it in a dream-like, unreal world, full of ghosts and demons and faraway kingdoms. Beauty and pure emotion matter more than psychological reality in this poem.
The angels and demons offer a way for the speaker to soften the reality of death. By blaming spirits for killing Annabel Lee, he can soften the blow of her loss.