I've wondered about this for quite a while and I figured I'd put the question to you guys as legal experts.
The idea really became well formed in my mind when I was working on the printing press and would regularly read a Jewish newsletter for the Chicago area that we ran. It set me thinking about how valuable a resource a religious organization can be for it's members. They're really excellent models for how many non-market-based services can be provided outside of state action.
Prior to the major involvement of the state in things like charity (welfare), education, and health care, religious organizations were the major providers of these services. To some degree they still do provide these sorts of services and others which the state does not provide, such as social networking and adult education.
So, could you create a secular, tax-exempt, organization that has a set philosophy (humanistic, for instance) which provides adult education, social activities, private schools, scholarship funds, recreational facilities, counseling, etc., exclusively to members?