In doing some online research about the relationship between religious belief and charity, I found a statistic that makes a lot of sense in a desire-utilitarian framework.
People who, as children, are regularly taken into a social environment where the virtue of charity is praised and practiced are more likely to become charitable adults. Even if that child grows up to reject religion - to become an atheist - she will, on average, be a significantly more charitable atheist than the atheist raised by atheist or antipatheist (one who does not care whether a god exists or not) parents who never exposed their child to such an environment.
It is unfortunate that so many of those institutions that teach children the virtue of charity also teaches them contempt for others (homosexuals, atheists), encourages them to devote energies destructive towards their happiness, and teaches contempt for evidence and reason. However, those institutions are not to be faulted for their ability to teach charity.
These results are the results that desirism would predict. If you raise a child and expose them to an environment in which certain qualities are praised and others condemned, then the child will more likely (not guaranteed) grow into an adult who desires those things that were praised and who are averse to those things that were condemned.
The child who is taken religiously (pun intended) into an environment where charity is praised will become an adult who desires to perform charitable acts. The child who is raised by parents who stay home and engage in self-indulgence all weekend will more likely become self-indulgent adults.
Religions have been around for a long time. The vast majority of those religions that have been invented have since gone extinct. What we are dealing with now is a set of religions that have been tested and have proven themselves fit. These are the religions that have survived.
It would be irrational to look at the qualities that these religions have and reject all of them simply because they are associated with religion. Reason suggests that we take a look at what religion does, try to discover what it does that is worthwhile and what it does that is harmful, copy that which is worthwhile, and abandon that which is harmful. Reason suggests that we take those people who argue, "That is what religious people do, so we should condemn it," and look on them as people who are responding to the facts irrationally.
The practice of leading children on a regular basis into an environment where certain virtues are praised and vices condemned is one of the things that religions does well. Many of them to a particularly poor job of picking out what are, in fact, virtues and vices - identifying as virtues some traits that are not worthy of the title and condemning as vice some traits that should not be condemned. However, they do have a very effective way of passing those beliefs on to the next generation - and the next - and the next.
Which is probably one of the main reasons why we are still dealing with those institutions today.
It would be wise for atheist parents to set up groups that they drag children to (against the child's will) where the children are coerced into listening to lessons describing particular virtues and vices, where they will be expected to help participate in charitable behavior and other activities that exhibit virtues and warned against behavior that exhibits vices, and thus formed into adults who will be better members of their community than those children might otherwise have become.
These practices may very well explain why theists are more charitable than atheists on average.
It may also explain, in some cases, depending on the church, why they are more prone to hatred towards particular subgroups and why they share such a disrespect for reason and evidence. In all cases, these were the values that they were taught in this setting, and these are the traits that they carry with them into adulthood.
A similar institution that did a better job of distinguishing virtue from vice should be expected to have a better overall effect - raising children who not only become more charitable adults, but more tolerant and rational as well.