I'm by no means an expert on such matters, and cannot cite examples of particular shows, performers or venues, but I'm sure that there WAS raunchy entertainment on offer in Berlin in 1912 - if you knew where to look for it. The same would have gone for London, Paris, New York, Vienna...every taste would have been catered for although, unlike today, people generally chose not to shout about their more unusual or unorthodox predilections.
It absolutely goes without saying that any explicit or serious (i.e. not deliberately comical) reference to sex and cross-dressing in the mainstream theatre of the period would have been unheard of. In Great Britain the Lord Chamberlain had the power to ban any production of which he disapproved and I think once exercised this right to close down a stage version of Elinor Glyn's famously risque 'Three Weeks'.
British men have always loved getting themselves up in drag - just think of our pantomime tradition! And, throughout the Edwardian Era, Vesta Tilley was a major crowd-puller with her music-hall turn, in which she impersonated a dandy, top hat, tail-coat and all. Tilley was massively popular in both England and the States and, after her performance at the Royal Variety Show in 1912, was hailed by one critic as 'the most perfectly dressed young man in the house'. J. B. Priestley was rather less impressed and found Tilley neither funny nor convincing. I suspect that much of the appeal to late Victorian and Edwardian audiences lay in the sheer novelty of seeing a woman parading around dressed as a man.
It is interesting to note that, after her husband (a Tory MP) was knighted in 1919, Tilley became the eminently respectable-sounding Lady de Frece. But at no point in her career had she EVER cultivated a persona as overtly erotic as that of Marlene Dietrich in 'The Blue Angel'!
Nowadays, we are all more sexually aware and can detect a certain Sapphic appeal in cross-dressing turns like Tilley's. I don't know whether she herself had lesbian tendencies but I'm sure she had a large gay following. I believe that Sarah Waters drew on Tilley for some of the inspiration behind her famous 'Tipping the Velvet' which was adapted by the BBC four or five years ago.