"Conflict of loyalty" is a useful concept and term that gives us another dimension to work with than simply conflict of interest:
In our legitimate desire to avoid conflicts of interest in nonprofits, we typically make two oddly opposite mistakes:
But often, the "conflicts of interest" in nonprofits do not involve personal financial gain. Consider the board member whose commitment to rights for people with disabilities leads her to serve on the boards of two such organizations. At Board A she hears about a new grant opportunity that is opening up at a local foundation. Should she tell Board B about it, or is she obligated not to mention it?
Or what about the deputy director of a nonprofit theater who sits on the board of a battered women's shelter: two very different fields. He's just met someone he thinks would be a great board member for either organization. Should he suggest this person to both, or to which one?
In another example, what should we think about a senior staffperson who is married to the executive director . . . but who works as a volunteer?
Backing up a bit to define conflict of interest
We want to protect our nonprofits from financial conflicts of interest because, to take a simple example, we don't want a board member who is a stock broker to use his influence to move the nonprofit's investments towards his brokerage, and then to steer the nonprofit's investments towards financial products that pay high commissions. Similarly, we don't want a board member who is married to the executive director to vote on the executive's pay.
(A "benefit from interest" is another way to describe these types of situations -- and they can sometimes work in an organization's favor, for example, if the stock broker waives his fees for the nonprofit.)
But many of the situations on nonprofit boards are not about direct financial interests. They are about conflicts between loyalties to more than one organization or cause.
Add this or something similar to your conflict of interest policy:
"We acknowledge that conflicts of loyalty sometimes arise that do not involve financial gain. We encourage (but do not require) that relationships and affiliations that might result in a future conflict of loyalty be disclosed, such as serving on other nonprofit boards or for-profit boards. We know that relationships and affiliations have potential for both conflicts of loyalty and collaborative benefits, and open discussion of such situations allows for informed and thoughtful choices."
See also in Blue Avocado:
Jan Masaoka is publisher of Blue Avocado and the CEO of the California Association of Nonprofits (CalNonprofits) . Her books include Best of the Board Cafe  (Fieldstone Alliance) and The Nonprofit's Guide to HR: Managing Employees and Volunteers  (Nolo Press). She has caused many conflicts and is full of conflict herself.