Now, this isn't a comedy, but in a way it's a comedy of errors, in that most of the conflict is driven by the misunderstanding that people are on different sides when they're really not.
The Yuri/Angel conflict is mostly confusion as to what their goals actually are.
This is even made explicit in the show between Otonashi and Tachibana. No one has much reason to fight among themselves.
The doppelganger and shadow crises are actually opposition, but the real fight is between Yuri and God.