There is not a regulation that controls the interest rate you will pay on a deposit account. Some banks negotiate rates for certain (usually high dollar) customers. Also, there isn’t a regulation that would mirror fair lending, but I would argue that you need to apply the same principles and negotiate rates on an equitable basis, regardless of a prohibited basis, due to reputational risk.
There are prohibitions on preferential rates being paid to a director, officer, attorney, or employee. (https://www.law.cornell.edu/uscode/text/12/376).