We have a vague impression that tame times are more sex-segregated and wild times are more mixed-up -- the '50s picture of the girlfriend and her gal pals sitting around a tupperware party while the boyfriend and his buddies are out having a drink, vs. the '70s picture of a bunch of boys and girls gathering to shoot the bull, get a little drunk, and then go out dancing. The segregated world shows less trust between the sexes, the mixed one more.
This pattern is hard to notice about the present. I might write up more examples later, but just consider that most of young girls' serious / long-termish guy friends are mostly gay. That's the only way they'll trust a guy enough to hang out with him in a variety of friend-like contexts. It's either that or just about no guy friends at all (again, ones whose relationships are as involved and even as close as those with her chick friends, not just an acquaintance).
To find out when the change happened, ideally we'd have annual survey data about how many gay friends a girl has. Unfortunately we don't. So let's look to pop culture that aims for some degree of contemporary realism. When did the "gay best friend" become a stock character? Well there's Mean Girls from 2004, where the only guy who isn't a boyfriend to someone is flaming gay. Before that was Will & Grace, which began in 1998, although I've never watched it, so couldn't say if there are substantial non-gay male friend roles. For sure there's Clueless from 1995, where the only guy who plays a strictly friend role is gay. The year before that produced My So-Called Life, where again the only guy in a friend role to girls is gay.
Heathers from 1989 was very insightful and captured a zeitgeist, and even shows the beginnings of the sex-segregated world that was to develop during the falling-crime times of the '90s and 2000s -- yet no gay best friend. Most of the teen movies from the '80s show mixed-sex social circles, such as Fast Times at Ridgemont High and A Nightmare on Elm Street, although not if the point was to emphasize how socially inept they were (like Weird Science or Revenge of the Nerds). The basis of the running gag of Mr. Roper's cluelessness in Three's Company was how unlikely it was in the late '70s and early '80s for a couple of cute 20-somethings to have a gay guy as their closest friend and housemate.
I can't think of too many examples to test from 1990 to 1993, but it's pretty clear that this is a rising-crime vs. falling-crime difference, with greater trust between boys and girls in the former and less in the latter. If homosexuality isn't socially acceptable, girls will hang out just with each other (1950s), whereas if it is acceptable they'll hang out with guys provided that they're gay ('90s and 2000s).