Final answer:
Insignia not authorized on the ACU include non-military patches, unauthorized foreign military insignia, commercial logos, sports team logos, and political insignia. Only official and authorized badges and patches related to military service should be worn, as regulated by Army Regulation 670-1.
Step-by-step explanation:
Some examples of insignia that are not authorized to be worn on the Army Combat Uniform (ACU) would include items that are not part of the official uniform regulations. These can range from non-military patches, insignia from other countries' armed forces unless authorized during multinational operations, or organization-specific items that aren't recognized by the U.S. Army. Another example would be commercial logos or sports team logos, as well as any political insignia. The ACU should only display official rank, name, service, and authorized badges and patches that pertain directly to the soldier's service and achievements within the military. All adornments need to comply with the regulatory guidance provided by Army Regulation 670-1, which governs wear and appearance of army uniforms and insignia.