Back the Blue Act of 2023 This bill establishes new criminal offenses for killing, assaulting, and fleeing to avoid prosecution for killing a judge, law enforcement officer, or public safety officer. Additionally, the bill expands the list of statutory aggravating factors in death penalty determinations to also include the killing or attempted killing of a law enforcement officer, judge, prosecutor, or firefighter or other first responder; broadens the authority of federal law enforcement officers to carry firearms; and limits federal court review of challenges to state court convictions for killing a public safety officer or judge.