1872 was the first election when the Democrats were more left-wing on economics. After 1896 an economically right-wing Democrat became the exception rather than the rule.
Although I'd say on social issues the Democrats were not more liberal until the 1950's.
The Republicans have always had a puritan streak of sorts, and the whole Bryan episode was much more a fluke than an overall indicator of where the Democratic party stood. Now, you can argue whether that puritan streak was a force for conservatism or progressivism, but it was there.