Your wash cloth appears to be civilian issue, though contrary to the previous posters wash cloths were issued to all soldiers in wwii and even today.  Navy and coast guard are white.  Army is olive drab    NothingYuk” about a washcloth unless it wasn’t cleaned 

. 12 actors who fought in Normandy.       Norman D. Landing, Forum Normandy Correspondent, 17 May  2O26.   ..    

. 100 female actresses that supported the troops in WWI & WWII       Norman D. Landing, Forum Normandy Correspondent, 17 May  2O26.   ..

It certainly “could” have been used for that purpose, but I think it’s more of a repro aimed at the collector market.  

These are rare, but not to the level of only a handful exist right? I own one and I've seen 2 or 3 for sale at various places just in the past year. 

Welcome to the Forum!   It is hard to judge the originality of the painted insignia from the photos, but they are not US.  Maybe British...they had a complicated system of unit markings.     The helmet shell being US made is not surprising.  I am trusting your identification of the stamped markings, but steel helmets were something that were made for the British in American factories before the US entered the war in 1917.  

The ANG had four F-100 units sent to Vietnam and two to Korea in 1968 due to the Pueblo Crisis. An in-country active duty unit, the 355 TFS, was mostly manned by ANG pilots. Your patch above was when the KANG had the F-105 training role in the 1970s.   Randy

I believe my family and I returned to CONUS aboard the USNS Geiger in August '63, Bremerhaven to NYC. Can anybody confirm 'this route and date?