I never really noticed. Sadly, I was too busy noticing how everyone in the rec deck were starting in Kirk's direction... apart from not just the two gossiping folk in the lower left corner but the really tall enterprising chap who was looking over and downward at another crewmember's goodies... what, no retake? Then again, so many scenes reveal those pajama outfits making it too understandable for anyone to look (what were the costumiers (clothiers?) on at the time, anyway?!).
But I never noticed some of the people wearing civilian or non-military attire dotted around the scene. As postulated above, I agree that it's a civilian badge of some sort.
Had the same movie been made 30 years later, somebody would have put in Waldo. But in a red outfit, Waldo would have stood out in that beige and sky blue blandfest...