Even though the game assumes that the authority is religious, do you think the non-religious players could get in the right frame of mind by seeing it as a game about the limits of authority in general (i.e., not specifically religious authority)? As a non-religious person it seems like I would be able to draw from the quandaries of having total moral authority and moral doubt. Or do the moral perspectives that the players bring need to be religious since religion is such a part of the setting? (Hopefully I'm asking that clearly.)
Also, my group has a wide spectrum of political and religious views. Do you think it works well in groups of mixed morals or is there too much room for arguments to spill off of the table and into the real world?
I don't think that the specifically religious nature of the moral questions is that important to the game--it's important to the setting, and to many of the characters, but you could totally play a Dog who is secretly atheist but cares about the moral issues. Or you could as a non-religious player play a religious character, and again engage with the moral issues as interesting issues. And then of course many alternate settings get away from the religious background entirely.
Re: a wide spectrum of views: I don't think that's necessarily a bad thing, but it goes to issues of trust and comfort. I would ask myself the question, "would I feel comfortable discussing a serious real-world moral question, with political and religious overtones, in this group?" If your response to the idea of a discussion of, for example, same-sex marriage, is "wow, that would be totally awful, we should never never never bring that topic up," then my guess is that having a Dogs game where a same-sex relationship was at issue would also be a bad idea. And if there are lots of topics like that, so that you have to steer clear of all issues of sex, gender roles, and morality, then you're playing with the least interesting parts of Dogs, and I personally wouldn't bother. If, on the other hand, you're like "Well, Sally and Joe will really disagree over that, with Jim having a different perspective, but we're all adults who are comfortable disagreeing over these sorts of things, and the conversation could be interesting..." then you might have a really fruitful game. It can also help for the PCs to have different attitudes from the players (the cognitive dissonance can be fun), but that can also make the game less "grabby," reducing the emotional punch--it's often said that you want a moral dilemma that's designed to grab the players, not just the PCs.
The tl;dr version: Be careful about it, that could cause problems, but it could work well if the players have a lot of trust and respect.
