Ensuring Equal Access to Shelter Act of 2019 This bill prohibits the Department of Housing and Urban Development (HUD) from implementing, administering, enforcing, or in any manner making effective the proposed rule titled Revised Requirements Under Community Planning and Development Housing Programs , published by HUD in Spring 2019, or any final rule based substantially on such proposed rule. The rule allows, among other things, shelter providers under HUD programs that permit certain single-sex or sex-segregated facilities to establish a policy by which such providers may consider an individual's sex to determine accommodation within or admission to a shelter or its facility.