What's with the Mao photograph on your avatar?
Are you actually a GOP or libertarian troll?
In any case, your question isn't completely accurate. A little historical research will show that most of the original "Progressives" were upper class, good-government, reform-minded Republicans -- at least back in the 1890s, when the Progressive Movement began.
You're obviously correct about Democrats championing many of the social welfare / social safety net programs of the past 80 years.
But before the Democratic president Franklin Roosevelt campioned social and economic reform in the 1930s, his distant cousin Teddy Roosevelt, a maverick Republican, also worked for government social programs and improved regulation of the giant corporations during his presidency from 1901 - 1909.
Other important Republican "progressives" during the first few decades of the 20th century included Sen. Robert La Follette of Wisconsin and Sen. George Norris of Nebraska. Still another early Republican Progressive was Sen. Hiram Johnson of California.
So historically, Republicans have SOMETIMES been on the side of reforms that helped the common people.
Since the 1930s and FDR's inauguration of the New Deal, however, most Republicans have come into the orbit of the super-rich, and since Lyndon Johnson's splitting of the once "Solid Democratic South" through the enactment of important civil rights laws, the Republican Party in the South has gone from being the party of racial justice and African American rights to being a largely racist institution.
So you're correct about today's GOP being a force for economic elitism and racial bigotry, for the most part. Yet it's important to remember that historically, Republicans sometimes have taken very different positions on these issues.