That seems a bit odd; I don't know whether it's customary. For a volunteer position, I think there would be serious problems with enforcing the noncompete. Perhaps if it was a prestigious and highly desirable position. It's as likely, though, that the noncompete is just boilerplate that somebody left in when the contract was cribbed from a for-profit, compensated board position.
When odd or questionable conditions come up in an employment contract (or other important contract), it's often a good idea to consult a lawyer. If one thing catches your eye, chances are, there's other stuff lurking in there that's worth knowing about. For your volunteer position, it may even be worth objecting to the noncompete clause. It might seem like it would never matter, but the law works in mysterious ways. Also, wonky contracts may scare off other volunteers, so it's in the organization's interest to have good, clear contracts that do what's needed, but nothing more.
Under most states contract laws, a contract is only binding if both sides get something. It is called consideration.
If you sign a non-compete agreement, it will only be binding if you get something in return - like a job, or money.
Arguably, any contract for a volunteer position is not binding because there is no consideration. I would also think it would hurt your Board recruitment.
My advice would be - don't do it. It doesn't help if it is not binding and might scare off some good folks!
Non-compete clauses are difficult to enforce in Oregon as it is. ORS 653.295 governs non-compete clauses and states that they are voidable unless they conform to the terms of the statute. Since you describe this as a volunteer position, and not a paid term of employment, it may not be enforceable. Non-competes apply to offers of employment. There is a salary requirement for Oregon non-competes as well, indicating that to be enforceable the employee must be paid in excess of "the median family income for a four-person family, as determined by the United States Census Bureau for the most recent year." You also do not mention whether the non-profit has any protectable interest, such as trade secrets or confidential information.