In administering any funds appropriated or made available for disbursement through the counties for welfare purposes, the department shall:
(a) Require as a condition for receiving such grants-in-aid, that the county shall bear that proportion of the total expense of furnishing aid, as is fixed by the law relating to such aid.
(b) Establish regulations not in conflict with the law fixing statewide standards for the administration of all state or federally assisted public social services, except health care services and medical assistance, which define and control the conditions under which such public social services may be granted or refused. All regulations established by the department shall be binding upon the boards of supervisors and the county department.