Oddly enough, in south Louisiana in the 60s we called them fruit loops. Never heard of fag tags.
I think this is one of those geographical dividers, whereby some people call them this, some people call them that, and some people will have no idea what you’re talking about.
Growing up in Texas, I saw them alot in junior high, and yup, we called 'em “fag tags”. I hardly see them anymore, so I guess I don’t have to worry about what to call them.
In southern California, circa 1964, they were usually called “fairy rings,” and you were supposed to rip them off–with or without the permission of the shirt-wearer.
Sorry, but I REALLY think the “aid to hanging up in locker” idea is bogus.
I think it had to do with protecting and preserving the back-of-the-shirt pleat, which would otherwise flatten out. Well, not really on those actual shirts, but perhaps on the shirts they were modelled after, setting a style.
Why?
I don’t know the answer to this one, but I know a man who does. Jean Paul Gaultier. He puts those tags on eveything! For an example check here (although that’s from the inferior JPH jeans line).
Anyhoo, I’ve just dropped him an e-maille, and I’m sure he’ll get right back.
Tell me you referred to them as fag-tags in the email, pretty please?
We always called them “nerd loops,” a term which will also offend a certain percentage of the population.
In my Champions campaign, people had loadbearing harnesses built into their costumes, and the nerd loops were actually steel cables that hooked into the harnesses so that my shrinking, flying character could fly up behind somebody, grab hold and give him a lift.
But I don’t think that’s what they’re for in real life.
What would JP know about fags? 
Update from JPG (if you’ll pardon my French)
Bonjour,
Il n’y a pas de raison fonctionnelle concernant la " TAB " appliquée au
dis des vêtements, c’est simplement un signe de reconnaissance sur les
vêtements de Jean Paul Gaultier .
Bonne soirée
Fruit loops. Sometimes girls (in the 70’s ?) would rip them off and keep them as trophies.
Peace,
mangeorge
Well, around here, the name “fag tags” referred instead to the little useless flaps on the shoulders of 80’s-style (Members Only?) jackets. I’ve always just called the thing you’re thinking of a “shirt loop.”
I think those jacket loops were called that because kids thought they looked effeminate or something.
I am pleased to have retained enough French knowledge that I was able to translate M. Gaultier’s response.
When I was a kid I somehow decided the tags in question were some sort of buttonloop, and that there were jackets out there that had large buttons on the back. But they had since gone out of style, and the loops remained.
I always found the “it’s just there, it doesn’t do anything” explanation unsatisfying.
A.k.a. epaulets.