We shared jackets on the last couple of bases I was on. One in the far east.
Not a big problem. But we had a pretty good program of regular cleaning.
If however you got one that was bad..maint. had spares and they would change it immmediately just switching the PLB.
We did however have aircon most of the time.
We also had enough flight suits issued (3) that you wore a "Fresh" one every day.
In chilly North Atlantic climes we each had our assigned immersion suit also with a very good cleaning program.
Also maint stocked ear pads for our Bose headsets so that was nice. They would usually last for a tour.