Responsible Consumer Financial Protection Regulations Act of 2013 - Amends the Consumer Financial Protection Act of 2010 (title X of the Dodd-Frank Wall Street Reform and Consumer Protection Act) to replace the position of Director of the Consumer Financial Protection Bureau (CFPB) with a five-member Commission whose members are appointed by the President, by and with the advice and consent of the Senate.
Prohibits the Chair of the Commission from making requests for estimates related to appropriations without the prior approval of the Commission.
Revises procedures for funding the CFPB. Eliminates the Consumer Financial Protection Fund and the requirement that the Board of Governors of the Federal Reserve System transfer funds to the CFPB from the combined earnings of the Federal Reserve System. Authorizes appropriations for FY2013-FY2014.
Directs the CFPB, in prescribing a rule under the federal consumer financial laws, to consider the rule's impact on the financial safety or soundness of an insured depository institution.