May a nonprofit racing association suspend and fine a non-member and deny membership in the association for asking for financial statements?
A nonprofit association would not be able to fine or suspend a non-member from “membership” benefits if the person is not a member. It wouldn’t be able to take away your right to vote, for example, if you don’t have a right to vote.
But if you are talking about suspending someone from participating in the association’s activities that are open to non-members (e.g. races), they can set whatever criteria they want for participation and suspend rights or impose fines for violations of their rules. It is not clear how asking for a financial statement would violate a rule, but who knows? You do have to wonder, however, about a group that would impose penalties for asking for information and not simply deny the request.
They can also normally deny membership in the association for whatever reason they want, so long as they are not a public accommodation and the denial is not based on membership in a protected class, and so long as they are not so economically significant that a denial would be a violation of antitrust laws.
If the organization has to file a Form 990 annual tax information return, of course, you can get a copy of the return and get a good sense of their financial condition. If you see anything you think might be criminal, you can complain to the state attorney general or local prosecutor. You can also discuss any issues you see with their members (who apparently haven’t asked questions before) and other participants in their events. Being seen as a bigger troublemaker is not likely to help you become a member yourself, but might help those who are already there to have a more open and responsive leadership.