I have to ask, why do these debates get bogged down in discussions of the respective characters? The characters are fiction, their players are fact. This has nothing to do with the characters and everything to do with the people playing them.
Players (including the DM) who agree to work together to make the game enjoyable for all participants can make any alignment combination work. The real question is "Can the players respect each others character choices, and find ways to enjoy the game that don't come at the the expense of others doing the same?"
The choice to work together and respect other people's choices is made first and foremost by the people playing the game. Everything else is secondary, and in the worst-case scenario, its players hiding behind their characters alignments/ethoi. Either you spend energy rationalizating ways for the group to work, or you do the opposite.
Let me say it again. It's not about the characters.
The game I currently run started with an elegant, aristocratic samurai, a flith-covered, insane, homeless street-shaman, an arrogant, bigoted, pyromanic alchemist, and an actual would-be hero. A recipe for campagin self-destruction, right? We're just around the two-year mark. It worked becuase the players were willing. If the players wanted to find reasons for their characters to behead, incinerate, and otherwise not work together, I'm sure it wouldn't have been difficult. Of course, the campaign strains credulity with some regularity, but find me a long-running D&D game that doesn't.
(You can read about their exploits in the Story Hour in my sig.)