One possibility is that churches, by being hypothetically obligatory to all, produce communities with approximate gender balance. By emphasizing inclusiveness they create a place for those who display sub-typical signs of selective fitness, people who hunter-gatherer instincts promote rejecting to avoid social contamination. With conformity they encourage such people not to drag the group down overly much. All of these features seem unlikely to form in natural communities if they are pursued explicitly. By default people join communities that appealed to their gender, communities that signaled status through membership or both. Most non-religious communities with ideals of inclusiveness also emphasize tolerance and individuality, leading to the less severe physical equivalent of trolls.

The closest thing that I have found to a secular church really is probably a gym. Far better than church in most respects, but not up to the standard this post seems to aspire to.