Just Avoid The Bullet

Now that all the research has been collected, we can confidently propose a better way to think about this myth. Religious people do not tend to be more altruistic than other people. Contrarily, “the students with high levels of intrinsic religiosity and doctrinal orthodoxy were less likely to help others or volunteer for the community” (Chang-Ho, 2006). Moreover, “intrinsic and orthodox religion foster compassionate and caring beliefs, yet the likelihood of actually helping others decreases as those religious orientations increase” (Chang-Ho, 2006).
How surprising! The explanation that follows:

“One of the popular explanations for moral hypocrisy is “overpowered integrity” (Batson and Thompson, 2001). To this theory, a person sincerely intends to be moral, only to give up this goal when the costs of acting morally become evident” (Chang-Ho, 2006).

Rather than diving into a debate concerning precisely what does – if not religion – foster morality leading to altruism, we shall instead alter the intention of the myth's statement. A more accurate claim would be: Genuinely religious people follow philosophies which can and do motivate altruistic behavior while atheists and agnostics can and do govern their lives by equally altruistic ethical principles of morality. Avoid any categorical comparison between the two in the first place.