I believe you are overinterpreting. That usage is equivalent to an American college student saying, "Ew, that's so gay" about Miller Lite Beer. The beer or its ingredients aren't gay; it's the drinking of it that is seen as uncool, and to insult it, Brits imply that drinking it is unmanly. Ginger beer is an actual drink made with ginger root, an alcoholic version of ginger ale. Also not gay.
Two of my favorite Britcoms are Monty Python and Are You Being Served.One of Python's skits features three characters,one of whom is named "Ginger" and is as fruity as they come.In an episode of AYBS they're serving a woman who wants to buy a sweater for her husband.At one point,when discussing the color she should buy,the woman says that her husband is "ginger"...meaning,in that context,that he's fair skinned and has either blonde or red hair.But on hearing her say that Mr Humphries gets an excited look on his face and,in case you're not a fan of the series,Mr Humphries is as fruity as they come.
I could be wrong here but I'm inclined to think not.
Any Brits who want to weigh in on this feel free so to do! ;-)
Below is a photo of "Ginger" from the Python skit I mentioned.
https://www.youtube.com/watch?v=JdCQwigh6H8