Why didn't Republicans become the progressive/ liberal party?

[Fuzzy Bear]

The Republican Party was the party of business from the Civil War onward.  Democrats were more socially conservative in many ways, but the GOP was the business party.

[Fuzzy Bear]

What was "progressive/liberal" and what was "conservative" at varying points in time?

The GOP was the Civil Rights party for 100 years.  They were the business party, but they were the big government business party.  V. O. Key once wrote how, the long period of Republican rule was due to more than the Moral Cause of the Union and the Victory that entailed.  "Sentiment clothed bonds of substance," wrote Key.  And those bonds of substance included protective tariffs for Northern industries (but not for Southern crops, save sugar), military pensions (for Union soldiers, not for Confederate soldiers), subsidies for railroads (which forged their routes to direct the flow of commerce away from the South, and free land under the Homestead Act.  Whatever you want to call these measures, they are not the acts of a "small government" party.

Likewise, the Democratic Party was the party of White Supremacy.  Literally.  It was a party where a Southern faction made a deal for "Home Rule" and the national party would leave the South alone when it came to segregation and voting rights abuses in exchange for electoral votes for President.  It was Wilson who cruelly REsegregated the Federal Civil Service.  And not all conservative Democrats were from the South; during the lean years of the Democratic Party, there was usually an alliance between Southern Democrats and the more conservative Democrats of the Northeast.  (Varina Davis, widow of Jefferson Davis, lived her final years not in the South, but in New York City.)