Exploring the conflict in Moxxie and Beelzebub fanfiction often hinges on the sheer improbability of their dynamic, which is exactly what makes it so fun to write. You've got this rigid, by-the-book imp from a violent but oddly structured mafia family paired with the literal chaotic, fly-ridden Prince of Gluttony. The most common tension naturally springs from their diametrically opposed natures—Moxxie’s need for order, respect, and artistic expression clashing against Beelzebub's realm of endless, mindless consumption and decay.
A lot of stories I've seen dive into the political nightmare such a pairing would cause in Hell's hierarchy. Think about it: a low-ranking Imp from the Pride Ring consorting with a Sin ruler? That's a recipe for external conflict, with other Sins, Moxxie's father Crimson, or even Blitzo’s I.M.P. crew causing problems. Internally, writers love to play with the idea of Beelzebub being intrigued by Moxxie's strange form of 'integrity' or his musical talent, something wholly alien to their domain, while Moxxie is simultaneously horrified and fascinated by the raw, unfiltered power and nihilism Beelzebub represents. It's less about romance and more about a bizarre, cosmic study in contrasts.
Some fics try to bridge the gap through shared outcast status—Moxxie never fitting in with violent imps, Beelzebub perhaps being bored or lonely atop the food chain—but the core friction is always that fundamental incompatibility. The endings vary wildly from tragic to strangely sweet, depending on how much the author wants to bend the canon personalities.