When I was doing my (late in life) BA degree in French and German at the University of Queensland, I knew a few students who were studying theology. The further they got into the subject, the more likely they were to become atheists! In the end, one student reckoned there wasn't a single believer in the department!
I mention this because these are the very same people who were once religious, and I cannot believe they became less charitable after exchanging religious belief for logic, or a scientific world view.
Also, some of the charities religious people give to, are religious charities, so there's a modicum of self-interest there. For example, I know from working in the local Zionist office, that most Jews quite rightly donate to Israeli causes, such as tree planting. But this again has some self-interest, because as Jew it is logical to support Israel, which might one day be the last safe place of refuge.