Recently, some of my Bank's commercial lenders have been contacted to be on the Board of Directors for entities the lenders and the Bank conduct business with. While there is a conflict of interest between the Bank and a Business, would it also be a conflict between a Lender and a Non-Profit, such as a civic organization or a church, because the civic organization has a loan with the Bank?

Any advice would be helpful. Thank you in advance.

As long as they personally were not involved in any loan decisions - no.