I agree with Dave - it would be wrong to assume that the English working classes in 1912 were necessarily unfamiliar with classical music. Then, as now, cheap concert tickets were always available for those who wanted them and the musical standard, even in the provinces, was frequently excellent. This isn't really my pet subject but I would recommend a look at J.B. Priestley's 'The Edwardians' for anybody with an interest.
I can't comment on the musical tastes of those who hailed from the further-flung corners of Europe but I imagine that the folk tradition would still have been prevalent in Scandinavia, Russia, Poland, Syria and elsewhere.
I assume that the Irish contingent in third-class would have danced to reels and jigs although I'm not sure if the revival of what I always think of as 'traditional' Irish music had yet to occur or was already going strong.
The ragtime craze was poised to explode in Europe in 1912 although the American working classes would have been familiar with its distinctive sound for several years already. Until the Great War, ragtime in England was really the preserve of the younger members of the fashionable upper and middle classes. Priestley, who was a young man living in, I think, Yorkshire during those years, was not able to recall any of his own friends dancing the Bunny Hug or the Turkey Trot. The Tango was the latest thing in 1912, and would go on to become nothing less than a global phenomenon for the next two or three years, but I'm not sure if the White Star musicians had it on their books yet.
Most West European and American passengers would have been able to execute a variety of dances (such as the waltz) with reasonable competence, since these would have been staples on programmes at balls and parties throughout the social scale. Likewise, nearly all the Anglicans and Catholics aboard would have been familiar with church music, just as we are all familiar with Christmas carols today - I seem to recall that Eva Hart, as a small child of seven, was delighted to join in her favourite hymn at the service held on the morning of 14th April.