I have heard foreign central bankers argue, “You can’t be independent in one function (monetary policy) and not independent in another (financial stability), without the nonindependence with respect to financial stability seeping over to weaken the independence of monetary policy.” I do not believe this is correct – as proof, I think each of us feels and is more independent in some of the decisions we make about our lives than in others.
Thus, I think the Fed retains its monetary policy independence despite its nonindependence with respect to financial stability policy. No doubt economists will long debate the appropriate institutional structure for financial stability authority.