A loan is an "account." The primary issue is whether the applicant is a "legal entity customer," not whether it is for profit or non profit.
If it's a corporation or other entity whose existence depends on a secretary of state(SOS) filing, the regulation applies. If it is registered with the SOS as a non profit entity, then you only need the information on the individual named under the control prong.
If the customer is not a legal entity; e.g. it's an unincorporated association (a made up term in most states) or just a gathering of like-minded people, it does not make any difference whether there is a profit motive or not, the regulation simply does not apply.
FinCEN went out of its way to exclude consideration of income tax status, but bankers keep insisting on dragging the issue into the equation.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.