Business of Insurance Regulatory Reform Act of 2020 This bill revises the authority of the Consumer Financial Protection Bureau (CFPB) over activities regulated by a state insurance regulator. The CFPB may not pursue enforcement against any person regulated by a state insurance regulator and offering a consumer financial product or service, to the extent that person is engaged in the business of insurance. If a person engaged in the business of insurance is regulated by a state insurance regulator but otherwise subject to the CFPB's enforcement authority, the CFPB must construe its authority narrowly.