"In areas administered by the National Park Service, an individual can possess a firearm if that individual is not otherwise prohibited by law from possessing the firearm and if the possession of the firearm complies with the laws of the state where the park area is located. 54 U.S.C. 104906. "
This post gave me the same question and I went and looked a bit. Looks like it: https://www.cdc.gov/poxvirus/mpox/vaccines/vaccine-recommendations.html