If anything, that is more representative of religion, as long as you say that's what god wanted (e.g. discriminating against LGBT people, trying to overthrow the government, etc.)
In contrast to non-theists, you simply employ a different way to ask yourself and society (albeit a subset of society which more rarely evolves their belief system to comport with the rest of society).
My “not necessarily” was intended for “You’d have to trust that society encoded the proper set of values and morals into the religion. Which sounds like ‘ask society’ but with extra steps, and also you’re asking the society of 1,000+ years ago instead of the society of today.” You don’t have to be asking society; you can ask yourself. As, I think, any sensible person does, regardless of their beliefs.
On the other hand, if you're asking yourself, and your answer isn't biased/affected by religion, then religion is by definition extraneous to your values and morals, which was my position in the first place.
The other side of the coin is, some of the worst atrocities in history were committed by people who asked themselves, and concluded that god wanted them to do it. Others were committed by people who asked themselves, and concluded that they wanted to do it. So religion doesn't seem to be either a good encouragement of good behavior or a good discouragement of bad.