The name of the band supposedly comes from their manager, Sandy Pearlman (according to Wikipedia and many other sites). It comes from poetry in which the “blue oyster cult” was a secret group of aliens that help to guide the development of humans here on earth.
Back in the 70s, though, it was commonly believed (at least in the area where I grew up) that “blue oyster” referred to eating oysters to improve your virility. There wasn’t any homosexual element associated with it that I ever remember hearing about, but there was definitely a sexual element to it.
Considering that the band members themselves apparently weren’t all that happy with the name (there’s a reference to that on the Wikipedia page) I have to wonder if the virility rumor was actually started by the band members, either to have a more “cool” origin for the name or so that they could get more chicks backstage after the shows or whatever.
The producers of Police Academy may have chosen that name for their gay bar simply because of its association with male virility. Just a wild guess on my part though.