In retrospect, whether you agree with it or not, Prohibition was the progressive, feminist point of view. When it comes to banning prostitution in Nevada, I am not sure if you can unambiguously make the same case. The same impulse is certainly there. One can make an argument that Harry Reid’s support for prohibition of prostitution is totally consistent with the progressive legacy. But the modern progressive movement isn’t unified in its moral objection to sex workers.
This is an example of how the progressive movement has morphed over the years. There could be big divides on the left over issues like pornography, prostitution, and other forms of traditional vice, but those divisions are driven below the surface by the unified horror aroused by the marshals of cultural conservatism.
In the latter part of the last decade, the (white) progressive movement in Philadelphia was largely driven by opposition to the expansion of gambling. Meanwhile, some in the (black) progressive movement saw gambling revenues as preferable to no revenues at all.