Again, party agenda has flipped despite the names, and have done so multiple times.
Unfortunately, names and labels seem to be all some people care about rather than what goes on underneath them.
The Democratic Party of at least the 1860s to 1960s was the conservative side and their descendants are those who are now called "Dixiecrats" that left the party in the 1960s, especially after LBJ passed the Civil Rights Act, and joined the Republican Party to which they also took in the far right religious nuts and others in order to pad their voter base through the "Southern Strategy" to elect Nixon and they have only become more and more right wing ever since.
The Republican Party of at least the 1860s up through Eisenhower used to be the progressive side, whereas in the eyes of the Republican Party today, ones like Abraham Lincoln and Theodore Roosevelt would be seen as really extreme leftists.
That's how much things have shifted behind the party labels.