Golf appears in Scots statutes of 1457 banning the game alongside football so that archery might be practiced. The word relates to Dutch kolf and German Kolbe, club. No Gentlemen Only expansion exists before the modern joke literature, and the earliest versions of the joke are twentieth-century.
The joke survives because the sport's actual exclusion history is real: many clubs barred women from membership for generations, and Muirfield only admitted women in 2017. The false etymology works as a compressed grievance, false as history, accurate as mood.
The pattern generalizes: backronyms often encode true social criticism in false linguistic form. Reading them as etymology fails; reading them as folk editorial succeeds.
A fake acronym that smuggles a complaint about exclusion into a word origin. Is that slander, or commentary wearing a costume?