A variant, but much like a specific form of tumor is a variant of cancer. I'd be willing to bet the young children of white supremacists don't donate much to solve starvation in Ethiopia and the kids of Zionists don't share pocket money with Palestinian kids as readily as among themselves.
The problem here really is ingroup/outgroup co-operation. One negative aspect of religious freedom is that there is more sectarian compartmentalization in US religion than there is in, say, Denmark or Britain where a state church exists. To be sure there are religious minorities in both places, but not the freewheeling ferment of competitive denominations we have. This results in increased zealotry in the ingroup, decreased ecumenicalism among the different denominations, and maximized stigma for the nonreligious. I would suspect a EWuropean do-over would show the same results for the religious, but given how few that would be, more cooperation over all.
Even in a pre-secularized Denmark, there may have been a couple of Catholics, maybe a Mormon, and several nonbelievers in a class but the vast majority, even of the latter, considered under the general Folkekirke rubric and therfore the "ingroup". With the US's religious balkanization and brutal competition for the shrinking universe of pew and more importantly plate fillers, religious groups work hard to separate who is "us" and "them", and it is human nature, even pre-religious, to only be co-operative with "us". Hence the correlation between religion and lack of widespread co-operation.