I suppose I should say here that I never intended my OP to be read in the abstract. To wit:

1. Religion attempts to teach morality and provide tools for solving moral dilemmas. I don’t think that’s controversial in the slightest; I’ve taught the high school class at my masjid for a decade, and about 80% of what I do is present them with moral dilemmas and show them how to solve them scripturally. And since I attended Catholic schools from K-12, I can tell you without any shadow of a doubt that they teach the same sort of moral lessoning in Catholicism.
2. So, I think it also noncontroversial to say that children who are taught moral lessons from religion grow up to become adults who use those moral lessons from their religious education in their daily lives — — whether or not they continue to be religious (where they would make a CONSCIOUS effort to use those tools) or become nonreligious (where the use of the tools exists below the conscious level. Put another way, “what seems right” to them will often be advised by those lessons that they think they’ve forgotten. Old habits are hard to break, after all.)
3. So, with that in mind……my OP could have been restated to say “If religion went away tomorrow, and nobody was getting any organized moral education……what sort of morality would we default to?” Ben suggests it would be based on “enlightened self-interest” (I am not sure it would be that enlightened, but never mind), while I think that people are more sociopathic than we believe, and that that would come to the forefront. Or, perhaps, morality and legality would become synonyms……which has it’s own issues.

Got to be honest, I don’t see any of that as particularly disagreeable.