we were just barely having an industrial revolution in 1912
Our 'Industrial Revolution' (which began in 1776, just like it did in England, BTW) was pretty over by then.
And such things were often based on class and social status. One thing that is almost impossible to realize in our day is how truly and deeply 'private' private life was, both in terms of what others knew, as well as in terms of what you shared with others. But I'm sure any number of Victorian groups like the Hellfire Club existed in the larger cities in the US, as they did in London going back to the 1880s. Certainly there were numerous cases of women passing themselves off as men.