The only real difference that I can see between Progressive-era Democrats and modern Republicans is in the area of immigration - while not all Democrats welcomed it (e.g. the Klanbake Konvention of 1924 that pitted conservative Southern Democrats against Al Smith's Irish-Catholic bloc), it's always generally been more pro-immigrant than the GOP, even in its more conservative incarnations.
Other than that, I see little difference. I suppose that the free trading Democrats of the 1890s-1920s would have opposed Trump's protectionism, but that's more symptomatic of one particular Presidential candidate rather than a whole Party.
Especially in the 1880s the Democratic Party looks a lot like relatively pro-immigration Tea Partiers, e g. their attacks on Benjamin Harrison's "billion dollar Congress".
Other than that, I see little difference. I suppose that the free trading Democrats of the 1890s-1920s would have opposed Trump's protectionism, but that's more symptomatic of one particular Presidential candidate rather than a whole Party.
Especially in the 1880s the Democratic Party looks a lot like relatively pro-immigration Tea Partiers, e g. their attacks on Benjamin Harrison's "billion dollar Congress".