The papers want to know whose shirt you wear.
What the hell does this mean, and what other lyrics make you go “WTF?”
It is a reference to the media interest in trivia. The main role of the astronauts at the time seemed to be PR for NASA. Some lyrics can provoke a WTF but not this one.
It means he’s a celebrity back on Earth, so the papers want to know what brand of shirt he wears.
I always assumed it meant he was really famous and the news magazines wanted to know what designer he wore.
Dammit. This song is going to be stuck in my head now.
I always took this as a sign of Tom’s celebrity status. Papers and magazines wanting to know which designers shirts he wears is an example of the minutia some fans want to know about the famous so that they may emulate them.
It means he’s famous, so the media wants to know…oh, never mind.
I bet he listens to Rio by Duran Duran…
“The papers” refer to the modern post impressionistic newspeak that informs confabulatory anomie. “Shirt” and “wear” are obvious neofeminist reactions against the patriarchal roles foisted on young girls who are forced into certain gender roles. Notice even with the lack masculine pronouns that the intuitive reaction to the song is to assume that “Tom” is an abbreviation of “Thomas” rather than "Tomasina, or even “Tomas,” also proving NASA’s neocolonistic . . .
Or like everyone said, it’s about media interest in trivialities.
In real other words, it means that you are too young to remember the obsessive press about the space program back in the 1960s.
For many years I thought this was “the papers want to know who shot you where”. Answers: NASA and space respectively.
Well, not being one who really even understands fashion trends or designer labels I assumed they were asking, you know, whose shirt are you wearing, as in: your own, your wife’s, another astronaut’s? It makes slightly more sense in the designer label sense. But only slightly. 
go read The Right Stuff - it will give you a great read, and an understanding of the media hoopla surrounding the space program.
It’s not about designer labels. It’s about trivia. Bowie was picking a stupid, totally irrelevant, bottom of the barrel question to exemplify the obsessiveness and the interest of the public in anything but the actual science itself.
For 20 minutes.
I always thought it was “whose side are you on” kind of question. Such as: Republican/Democrat or Bills fan/Miami fan or secretly a “commie”.
It really was just about the brand of shirt?
Oddly enough, the question was never answered.
Whose shirt DOES he wear?
I read somewhere it meant which football (soccer) team do you support, or whose jersey do you wear. The media wanted to know who his favorite football club was.
WooHoo! I was close!!!
I’m with Exapno Mapcase on this one.
Side question: is it possible Major Tom can’t get no satisfaction with his laundry detergent?