The term
"Friend of Dorothy" refers to a gay man.
It originated from The Wizard of Oz, and particularly Judy Garland who starred as Dorothy.
Judy Garland herself was a straight woman, but she was one of the most famous gay icon during her life. The reason is that she was beautiful, talented, and lived a tragic life, which mirrored the drama some gay men had in their own lives during the 1950's and 60's.
It's also unfortunate that straight guys who idolise Judy Garland are considered being gay. Many of whom probably grew up watching her movies since childhood.