Where does this term originate from, and why exactly does it get to mean gay men?
Clearly there is some link to the Wizard of Oz, but why particularly should Dorothy’s friends be gay?
Not Dorothy, per se, but Judy Garland is a big favorite among gay men. The Stonewall riots in NYC occured the week of her funeral.
I think it was also primarily code back in the days when gay men more or less were forced to be in the closet. I think it’s actually contemporary Hollywood slang from the Wizard of Oz days.
When I flew interstate with a gay friend years ago, he took me to a gay part of Sydney to buy the tickets. The travel agent was called F.O.D Travel. He explained the whole Friend of Dorothy thing to me then.
Judy married at least one gay man, and one of her daughters married two.
Allegedly.
So there is no supposition that the Lion, the Scarecrow, and/or the Tin Man were gay?
I think they became gay after they were “Touched by a Judy.”
The “Friend of…” tag is a borrowing of the phrase from “Friend of Bill,” which was shorthand for “I’m an alcoholic” when AA was first beginning. “Bill W” was one of hte founders of the organization and members, in order to identify themselves to other members in the outside world, refered to themselves as “Friends of Bill.”
I’m a Friend of Cecil.
the seasick seaserpent? 
Heh… the “Friends of Carlotta” scene from Dead Men Don’t Wear Plaid just flashed through my head.
Rachel Ward: “Do you know what FOC means?”
Steve Martin: “Yeah, it’s when a man and woman love each other, and he puts his…”
:: chalks up one more Arrested Development joke I never caught until after the fact ::
Among some gay men.
Armistead Maupin in Tales of the City referred to a gay couple as having an S&M relationship: Steisand & Midler.
I think the Judy Garland worship is generational within gay men.
Now it’s the vainglorious, brash, brassy, and ballsy that get the worship.
Of course, that’s just my perspective as one homo that can be extrapolated into an entire valid sample.
Sorry, Mockingbird, I didn’t mean to gereralize.
(Luv the S&M reference, though!)