Ensuring Military Readiness Not Discrimination Act This bill addresses the standards for eligibility for service in the Armed Forces. Specifically, the bill provides that any qualifications established or applied relating to eligibility for service in an Armed Force must not include any criteria relating to the race, color, national origin, religion or sex (including gender identity, sexual orientation, or sex characteristics) of an individual. Additionally, any personnel policy developed or implemented by a military department with respect to members of the Armed Forces must ensure equality of treatment and opportunity for all persons, without regard to race, color, national origin, religion, and sex (including gender identity, sexual orientation, or sex characteristics).