Indeed! As I have posted before on this list, I have been entirely unable to find a non-religious entity that will use me in any way than as a source of funds. Some of them even have FAQs that say that they appreciate my wanting to contribute time, but really, they would rather have my money and hire "experts" to do the work. Many organisations do not even respond to requests. When I was in college in Philadelphia I used to tutor non-maths major undergraduate students in mathematics... I was hoping to do similar things for school or college students, but couldn't find a way to do so (the local college(s) do not permit that sort of ad hoc thing). What the churches provide is also a community and a network, which enable such contributions by providing a framework.
--ravi