Progressive policies, in the early 20th Century, were pursued by politicians from the Democratic and Republican Parties, Bull Moose Republicans, Lincoln Roosevelt League Republicans (in California), and the United States Progressive Party.
When Teddy Roosevelt left the Republican Party in 1912 to form the Bull Moose Party, he took with him many of the intellectual leaders of the Progressive movement (but very few of its political leaders). It was at this point that the Republican Party became more committed to business-oriented and efficiency-oriented Progressivism. This policy was typified by William Howard Taft and Herbert Hoover.
Some forms of Progressivism were partially rooted in the Populist movement of the 1890’s, lead by William Jennings Bryan. Populists had a distrust of the concentration of power in the hands the elite, whether they were politicianas, corporations, families, or special interest groups. However, Progressive leaders (with one exception) opposed Populism outwardly. The only Progressive leader to come from the Poplulist movement was Bryan, himself. He was the only Progressive leader to espouse the Populist and Progressive movements.
Cultural Progressivism was rooted in Pragmatism (primarily developed by John Dewey and William James) in the late 19th Century. For Pragmatists, an ideology or proposition is true if it is proved to work satisfactorily. It should be noted, I think, that some things appear to work satisfactorily at the start, but have hidden negatives that do not appear until later. So has been the case with Progressivism.