Chapter 10, Sec. A.9 of the Auxiliary Manual, COMDINST M16790.1 (Series):
Auxiliarists may not wear any distinctive part of the uniform or official Auxiliary insignia with civilian clothing when not assigned to duty. This includes Personal Protective Equipment (PPE) that is marked with wording that includes, ―USCG Auxiliary‖ or any version thereof (e.g., life jackets, cold weather gear).
Also, see Sec. C.2.:
With the exception of authorized Coast Guard unit ball caps, Auxiliarists should avoid wearing uniform items that carry Coast Guard markings, particularly Personal Protective Equipment (PPE), work clothes, and organizational clothing. It is the responsibility of the Coast Guard unit that provides such uniform items to Auxiliarists to provide uniform items that are properly marked for Auxiliarists. Time and circumstances may not facilitate the availability of Coast Guard-provided uniform items that have Auxiliary markings. In such circumstances, Auxiliarists may wear the provided uniform items despite not having appropriate Auxiliary markings. However, all due effort shall be put forth to correct such circumstances so that Auxiliarists are provided uniform items with appropriate Auxiliary markings as soon thereafter as possible.