I would argue you need to make the 1930s more socially Liberal. Politically, it was New Dealism. But that is not the same as social progress. The 1920s were more libertine with issues of race and gender than the 1930s. If you look at that era, it was the female liberation of the flapper, the first youth rebellion, and pre-code films which often dealt with issues such as racial strife, sex, gender, etc. Yes, they ran up against the moralists and decency leagues, rebirth of the Klan and "Birth of a Nation", but can that be said to be different from the same forces the Boomer generation ran up against in the 1960s, which is considered a liberal era? By the time you get a few years into the 1930s, the mood had changed by the Depression, further imposed upon by the Second World War, and wiped away by a Post-Depression / Post-War era of keeping your head down and enjoying normalcy you had not for 20 years; which spanned the development period and youths of many people. If you were 16 in 1929, in 1945 you were 32; In 1953 (just for the argument of the Eisenhower 1950s after Korea, Truman, the Post-War Recession, etc) you were 40.
In summary, my argument is that the 1930s up until the 1950s or 1960s (depending on the area) were not socially permissive or progressive. Even though economics and the scope and idea of government were New Dealerism.