Well, no, Boy George et al were actually gender benders, not sex benders. They were men who wore the trappings of femininity
Put it into the context of the kids, parents/grandparents of the time. There was a lot of "is it a boy or a girl" "does it know what it is ?" dark muttering going on.
Most people would have blinked like a confused owl if "gender is a social construct" were presented to them.
Back in the day what you wore, what you did, how you expressed yourself had more acceptance as being a natural, normal, necessary part of your sex.
Which is why effeminate boys and men got a lot of "he thinks he's a girl/woman! Ha ha ha" style bullying going on in their obit. Same for less feminine women.
My poor cousin got a lot of stick. Her status as female was under constant attack. She got a lot of "well if you try to look like a boy we'll hit like you're a boy". For their perspective she was trying to step out her sex, not gender. Cos clothes and interests belonged to sexes.
Feminist theory didn't have a huge following in many circles and the media/technology of the time wasn't making it particularly accessible to the masses.
So for most people sex was gender and gender was sex. Two words, same thing, as far as a great deal of ordinary people were concerned.
The Red Tops may have known what they meant by the headline. But they also understood that most of the readership would conflate sex & gender, viewing them as having the same meaning, but one rhyming better with (the not so subtle dig laden use of) bender.