How did public life in the United States change as a result of the New Deal, and the World War 2 domestic mobilization? Viewed together,...

The Progressive Era was the period in the US from about the turn of the 20th century to the end of WW1, give or take a few years in each direction. Often it is taken to end in 1920 with the passage of the 19th Amendment granting women the right to vote.

During this period there was a great deal of social change, led by widespread activism for the rights of women and minorities and driven by an overall heady sense of optimism for the world's future as industrial technology was finally raising the standard of living to build the world's first true middle class.

WW1, at that point the bloodiest conflict in human history, created a profound sense of disillusionment from this optimism. Those who had once believed that technology could only make human life better had just seen technology destroy human life on an unprecedented scale.

Then came the Great Depression and further disillusionment; but this was followed by renewed hope with the New Deal, which radically expanded the role of government in American life from a "night watchman" state designed only to defend against aggression into a modern "welfare" state designed to make people's lives better and protect them from a broader set of risks such as illness, disability, and poverty. This solidified the middle class and expanded it dramatically.

WW2 interrupted this process somewhat by shifting essentially the entire economy and society into full war mobilization---and like the previous World War, created mass disillusionment by unprecedented bloodshed. Government spending in the US as a portion of GDP has never been higher than it was in WW2, with nearly all of that spending going toward the military. Unemployment was also the lowest it has ever been.

But WW2 did not reverse the expansion of government (simply augmenting it with a militarization that continued to expand during the Cold War and has only very recently begun to retreat), and the success of the New Deal before the war (as well as perhaps the success of the US military in the war) had permanently changed the way that Americans viewed the role of government. Programs like Social Security laid the foundation for a later expansion of even broader social insurance programs such as Medicare.

Viewed as part of the same process, both the Progressive Era and the New Deal involved both a large expansion of government and large shifts toward equality in representation and income. Income inequality peaked just before the Great Depression, and by the end of the New Deal reached the lowest level it has ever had in the United States, remaining near this level until the 1970s.

In particular both eras substantially expanded the rights of women; granted the right to vote in 1920, and then given the opportunity to work in factories (one of the central reasons the US had such overwhelming industrial superiority in WW2 was in fact the large number of women in factories), women realized that their subordinate status to men was not a necessary fact of nature but a policy decision, and ever since have fought hard against any policy that would seek to return them to subordination. Feminism would probably have ultimately prevailed anyway, but without the support of the New Deal and the employment of women in WW2, it probably would have taken a good deal longer, as it did in Korea and Japan (and in many countries, especially in central Africa, it still hasn't).