Russ Roberts' latest podcast with Dave Rose touches on this. My paraphrase: utilitarian morality does not lead to the greatest good. It works well in small groups (they used 25 people as a guideline) but fails in very large groups. This makes sense: for large group cooperation, coordinators need to correctly predict motivations of the people involved. If people can be made "mechanical" in the sense that they will do what they are told reliably (because they have a rule morality that tells them to), then larger organized efforts can succeed. If people defect locally from prioners dilemmas, the rate at which this happens creates an upper limit in the size of effective cooperative organizations.

I would say that religion is certainly a source of rule based morality on net. Rationalists (tm) pursuing their personal utility are often ready to defect from rules that they conclude come from outside their utility functions, or are at odds with their utility functions. Since we have a rather larger group of us on the planet than ever before, a path for removing religion might need to be carefully designed to not bring about the collapse of a lot of cooperative endeavors, to not bring about a collapse from rule-based to Rational (tm) utilitarian behavior on the parts of broad subpopulations.

Since I may not comment on the David Rose Russ Roberts podcast anywhere else, I will say here that I sure think it is at minimum ironic that the argument against utilitarianism as a moral system is that it is not as productive as rule-based moral systems can be. That is, the argument against utilitarianism is that it does not produce maximum utility. That is pretty much the only kind of argument against utilitarianism that might ever succeed with me.