Conscience Objections to Negligent State COVID-19 Inoculation Edicts Need Constitutional Enforcement Act of 2023 or the CONSCIENCE Act of 2023 This bill generally prohibits state and local governmental COVID-19 vaccine mandates that do not provide religious exemptions. Specifically, the bill prohibits state and local governments from establishing COVID-19 vaccine mandates that (1) place a substantial burden on the religious exercise of an individual or entity; (2) do not treat a religious exercise or condition the same as a nonreligious exercise or condition; or (3) exclude or unreasonably limit religious exemptions. An individual's refusal to receive a COVID-19 vaccine, or an entity's refusal to institute COVID-19 vaccine requirements, on the basis of a sincerely held religious belief is considered to be religious exercise. The bill establishes a private right of action and authorizes the federal government to bring civil actions for violations. The bill applies to any mandates adopted before, on, or after the bill's date of enactment.