Community Care Core Competency Act of 2017 This bill directs the Department of Veterans Affairs (VA) to establish a program to furnish continuing medical education material to non-VA medical professionals, with the goal of: (1) increasing knowledge and recognition of medical conditions common to veterans, and (2) improving outreach to veterans and family members. The program must include education on: (1) dealing with patients who are veterans or family members; (2) identifying and treating common mental and physical conditions of veterans and family members; and (3) the VA health care system. The VA shall: (1) carry out such program for five years on a VA website at no cost to participating non-VA medical professionals, and (2) ensure that the program is accredited in as many states as practicable.