The argument from the Christian community seems to stem from the ability to play as "evil" characters, in addition to the "polytheism = evil" argument. There are also sprinkles of "games of chance" and the idea of the DM as a "god." This sometimes devolves into the "evil = devil worship" argument, and is merely from a lack of understanding.
When confronted for playing D&D, I often argue that Monopoly is more like devil worship.
Christianity has a semi-rigid ideal of the benevolence of the common man, which is a lot more in line with D&D than they sometimes think. A good DM will use his godlike power to teach your character (and sometimes the players) that life is filled with consequence. If you die because you stumbled into a Lich's hideout, it's both bad luck and your own damn fault for poking around looking for loot. Similarly, playing as an "evil" character doesn't necessitate worship of evil gods, but rather indicates a character's nature to defy the laws deemed "good." Evil campaigns rarely last more than a few sessions before everyone dies, or kills each other. This is because the game is balanced toward a "good" playing style. Being a team player means your team wins.
Monopoly, on the other hand, has always been the source of an unreasonable argument about the selfishness of others in my experience. Often, the game ends with one person wielding godlike power over the other, who winds up tossing the board in the air with much anger. It also encourages selfishness, since there can be only one winner of the game. It is also a game of chance, and is essentially a game of money worship. Seems to fly in the face of Christian "family values," yet Monopoly is marketed as a family game.