How did populism influence the social structure of the US in the 20th century?

This is a difficult question to answer, because in some ways populism had different, even contradictory effects. Populism in the nineteenth century was aimed at rearranging the social structure, or at least reforming politics in such a way as to help people who were hurt by the economic developments of the so-called "Gilded Age." The Populists promoted restrictions on massive corporations, especially banks and railroads. They pushed for currency reform that favored ordinary people. They wanted the federal government to intervene to help sustain farm prices. Some even demanded fundamental reforms to the electorate, including direct election of senators and suffrage for women.
Populism declined at the end of the nineteenth century, but many of the reforms they demanded were eventually implemented by Progressive reformers or, in the midst of the Great Depression, the New Deal. But populism after the Second World War became something different. In the wake of the civil rights movement, it was deployed to tap into white outrage at African American gains, which were portrayed as having occurred at the expense of working-class white people. Politicians like George Wallace deliberately appealed to the conservative mores of working-class and rural whites, a strategy perfected by Richard Nixon and Ronald Reagan in a series of presidential elections. Unlike the nineteenth-century populists, who demanded government intervention to curb the abuses of corporations, these new politicians cast interventionist policies as inefficient, un-American, and ultimately benefiting people other than working-class whites—African Americans, immigrants, and others. As Reagan said in his first inaugural address, "[g]overnment is not the solution to our problems. Government is the problem."
At the same time, they also claimed that cultural changes had moved the nation away from its traditional values. This combination of an populist appeal to "traditional values" and pro-business and corporate policies proved to be a very effective strategy. In this way, populist appeals were put to precisely the opposite effect, and the policies they won support for were, in effect, intended to maintain the social structure was it was. Indeed, massive tax cuts and relaxed regulations contributed to the accumulation of wealth at the top of the social structure more than almost any other period in American history.
https://www.presidency.ucsb.edu/documents/inaugural-address-11