Secure Access for Essential Reproductive Health Act of 2023 or the SAFER Health Act of 2023 This bill prohibits health care providers and insurance plans from disclosing in a legal proceeding an individual's personal health information related to an abortion or pregnancy without the individual's valid authorization. The prohibition applies to federal, state, local, and tribal proceedings, including civil, criminal, administrative, and legislative proceedings. The bill provides limited exceptions such as if the information is necessary to investigate physical harm to the individual. Further, the Department of Health and Human Services must conduct an outreach campaign to inform covered entities and the public about the prohibition.