Wearing Our Badge in Uniform

10 U.S. Code § 1123 - Right to wear badges of military societies

(a) A member of the Army, Navy, Air Force, or Marine Corps who is a member of a military society originally composed of men who served in an armed force of the United States during the Revolutionary War, the War of 1812, the Mexican War, the Civil War, the Spanish-American War, the Philippine Insurrection, or the Chinese Relief Expedition of 1900 may wear, on occasions of ceremony, the distinctive badges adopted by that society.

(b) A member of the Army, Navy, Air Force, or Marine Corps who is a member of the Army and Navy Union of the United States may wear, on public occasions of ceremony, the distinctive badges adopted by that society.

The regulations for each service on this varies but the law authorizes it for all services except the U.S. Coast Guard. The law was originally passed in 1894 and again in 1907 when the ANU removed the word "Regular" from their name.