Of course the early 1900's was a time when women's rights where taking a forefront through the Temperance Movement, the Womens Christian league, etc etc etc
Suffrage happened in this time period, Women were organizing and getting involved( Esp in the temperance movement, because women were usually the primary victims of alcoholism).
We should also note that Columbia, according to content ommitted from the game, but hinted at in posters, had an actual elected government with comstock either serving as permanent commander in chief/ prez/ or as a figure head for most of the day to day affairs, letting his elected gov govern while he works the master plan.
Of course non whites were disenfranchised.
From the outside it looks almost like taudry liberal shit.
Until you realize the Vox Populi are a double edged sword, and in a way more oppurtunistic and capable of wrong than their oppressors.
It's hinted in the universes where Booker is killed - either in the attempt to rescue her in the universe where they move her to a more secure location and Booker becomes a Vox Populi hero posthumously, or the one where he is killed by the handyman near the end, that the Vox Populi sympathizes with Elizabeth in the end, they free her, kill Comstock, and she still becomes what she was prophesized to do - bring about the apocalypse and destroying the cities and mountains of man - REGARDLESS of whether Columbia is won by the Vox who disenfranchise it or not.
It becomes obvious to her that both of these options end in the same result, and the only way to stop it all is to kill Booker before he becomes Comstock - in all universes
But yeah, I think they could have made this more open world, more exploratory.