Religious groups used to offer association type plans to those who joined their associations, but this always a situation where the sick and chronically ill would buy a plan with a guarantee of issuance. This would drive up claims and the insurance carriers would sever their contracts with the association. The two best examples of this in California were the California Bar Association plan and before that, the B'nai Brith plan. Claims due to easy acceptance drove the insurers out of the market place.
Anytime you see a plan offered through an association, union, or religious organization that requires no health questionaire nowadays, it usually is some sort of fraud.
The reason why religious organizations cannot offer a group plan is that it would not conform to the rules that allow qualified group health plans to be sold. Membership is not enough, there must be an employer-employee relationship to establish group coverage.
That is not true. See the Medishare pland.