Certainly, this is a CIP issue, but it's a fundamental loan quality issue too. The question for the lender is: "Who is it that you loaned the money to; i.e. who will we sue if we do not get repaid?" Somebody should be really upset that this issue did not surface until the loan was being renewed.
Evidence of affiliation with a particular sect is not evidence of legal existence. You are looking for evidence that they exist in the eyes of government, not the eyes of people with similar beliefs.
Churches are not required to register with the government at any level. Issues like "freedom of religion" and "separation of church and state" would preclude any such requirement.
However, as John noted, entities; e.g. corporations, may be required to register with the state. If the legal entity happens to have a religious theme or purpose that does not make any difference, the entity still has to register.
If the organization is not a legal entity, but claims tax exempt status and tells its supporters their contributions are tax deductible there is a letter from the IRS acknowledging their existence somewhwere...