A utilitarian's reasoning doesn't present a moral argument without (necessarily) the need for religious support?
I think there are a bunch of problems with utilitarianism, particularly what I would call pure utilitarianism, in which motive is divorced from result. As far as motive/intention-based utilitarianism, they tend to be a pretty muddled mess that inject human action at or near the start of the analysis, which is incompatible with physicalism/OR.
To expand on the problems with pure utilitarianism, let's say I am a highly trained special ops soldier sent on a reconnaissance mission to Nazi Germany and, after months of careful planning and determining the absolute safest way to carry out my objective, I blow up a building and kill Hitler along with two other innocent bystanders. Have I acted morally? Maybe, maybe not, but I think there's a reasonable argument that I have. On the other hand, let's say I'm a citizen of Berlin in Nazi Germany, and get in a terrible argument with my wife. After she leaves the apartment, I grab my firearm and try to shoot her as she's walking down the street. However, my aim is terrible, and I accidentally shoot and kill Adolf Hitler, along with the same two bystanders. Same result, same amount of happiness or utility created, but a very different action from a moral perspective.
I don't think accounting for intention solves the issue. A third time, I'm an insane person, or perhaps a very careless one, living in Nazi Germany. On seeing someone outside my window, I become convinced that they are Hitler, grab my gun, and shoot them. That person, who was most definitely not Hitler, dies instantly. However, by pure happenstance, and unbeknownst to me, Hitler is walking directly behind that person, and my bullet passes through my intended victim and kills the actual Hitler as well. So to combat that scenario, you would have to introduce some concept of warrant, and so on and so forth, and we progress ever further from a physicalist definition.
I also think a vanishingly small number of people actually are utilitarians. Dawkins spends a chapter or two laying out utilitarianism as a valid alternative to theism-centric morality in
The God Delusion, but at the end he confronts the dilemma of whether he should shove a very fat man onto the railroad tracks to stop a runaway train with four people on board that's about to run off a cliff. Under a utilitarian viewpoint, as Dawkins admits, the correct answer is to push him, but Dawkins can't pull the trigger. I believe that utilitarianism tends toward an objectification of human beings and an oppression of minorities that few people are comfortable with.
Even if you did push the fat man onto the tracks, and might feel that your action was justified, I doubt very much that most people would view it as an unquestionably moral act. Contrast that to, say, putting yourself in great moral danger by driving onto the tracks, boarding the train, and rescuing three of the passengers, or even rescuing all four and going over the edge yourself. The end results would be the same (3 lives saved, 1 lost), the intention would be the same (save the passengers), but I daresay that most people would see and judge the moral implications differently. Maybe I'm wrong about that, but I really don't think so.