Ensuring Military Readiness Act of 2023 This bill requires the Department of Defense (DOD) to prescribe regulations regarding military service by individuals who identify as transgender. Under the regulations, individuals who identify as transgender with a history or diagnosis of gender dysphoria must be disqualified from military service, with some exceptions. (The bill defines gender dysphoria as a marked incongruence between one's experienced or expressed gender and biological sex.) The regulations must provide exceptions for such individuals if they have been stable for 36 consecutive months in their biological sex prior to accession, or diagnosed with gender dysphoria after entering into service if they do not undergo transition procedures and remain deployable within applicable retention standards for their biological sex. Under the regulations, members of the Armed Forces who have been diagnosed with gender dysphoria may continue to serve in their biological sex (regardless of any changes previously made to their gender marker in the Defense Enrollment Eligibility Reporting System, or DEERS) and receive medically necessary treatment for gender dysphoria. However, such treatment may not include gender transition procedures. Individuals who identify as transgender and who seek or have undergone gender transition are disqualified from military service. Additionally, individuals who identify as transgender, do not have a history or diagnosis of gender dysphoria, and are otherwise qualified for service may serve in the Armed Forces in their biological sex. DOD must prescribe regulations updating DEERS to require the gender markers for members of the Armed Forces to match their biological sex, regardless of any previous changes.