TwoSix
Everyone's literal second-favorite poster
I'm sorry, but that seems like an extremely limited perspective on what backstories are "allowable". It doesn't mean ignoring the background, it means embracing it and shaping it into an interesting premise. And honestly, I find your comment about "jealous gods" to presuppose concepts about the nature of religion in the game that I do not share.The "fluff" on both the classes makes it pretty clear that their magical abilities are outsourced. Combining the classes requires ignoring that background. Mechanically it will work, the game is written that way so the DM can freely change the fluff around. But the default assumptions of the game make it pretty clear that this particular combination isn't going to go very far at many tables.
1) It's quite possible for a pact patron and a god to have their goals in alignment. The cleric/warlock in question might be a handpicked agent of the god's proxy. A cleric of Asmodeus / fiend pact warlock makes perfect sense to be aligned, as well as fey pact warlock / cleric of Corellon or any other god of the Seldarine.
2) Clerical power need not be granted with any particular strings attached. The remote dieties of Eberron don't particularly care what you do with divine magic, for example (and are PHB official).
3) Likewise, a warlock pact may not be a choice on the part of the PC. Perhaps a particular child is born into a family curse of a pact with a devil (I'm thinking of Moorcock's Von Bek family as an example), but turns to the church in order to maintain his hold on his very soul. The chain pact familiar could be a very literal "devil on his shoulder". The pact sword could represent the constant temptation to violence. Perhaps every time the character strays from the righteous path, he is granted more power to further his temptation (represented by gaining more warlock levels).
In general, backstory should be deployed to further the character's development and conflict, and provide new narrative hooks, and never to limit a player's choice of mechanical expression.