DEI Pay Cap Act of 2023 This bill prohibits the Department of Defense (DOD) from appointing or employing a military or civilian employee with a rank or grade in excess of E-5 base pay or GS-5 (not adjusted for locality) for any position with specified diversity, equity, and inclusion components. Specifically, DOD may not appoint such individuals to positions with duties that include (1) developing and implementing diversity, equity and inclusion policy; (2) leading working groups and councils to develop diversity, equity, and inclusion goals and objectives to measure performance and outcomes; and (3) creating and implementing diversity, equity, and inclusion education, training, and workshops for military and civilian personnel. Any military or civilian employee who has been appointed to such a position and holds a rank or grade in excess of E-5 or GS-5 must be reassigned to another position not later than 180 days after the enactment of this bill.