Arrest Murderers not Ministers Act This bill specifies that in order for the federal government to prosecute individuals for violations of the Freedom of Access to Clinic Entrances Act (which prohibits forceful or threats of forceful interference with an individual's access to reproductive health services or exercise of religious freedom), the violation must involve intentional physical injuries or damage. Any funds that would have been used for prosecutions that are prohibited under the bill must be used to prosecute individuals who commit violent crimes or other specified offenses.