Protecting Access for Hunters and Anglers Act of 2023 This bill bars the Department of the Interior and the Department of Agriculture from prohibiting or regulating the use of lead ammunition or tackle on federal land or water that is under the jurisdiction of such departments and made available for hunting or fishing. The bill makes exceptions for specified existing regulations and where the applicable department determines that a decline in wildlife population at the specific unit of federal land or water is primarily caused by the use of lead in ammunition or tackle, based on the field data from such unit, and the state approves the regulations.