Oh great, another one of these threads...the Republicans were inarguably to the left of the reactionary Democrats in the 1850s, 60s, and 70s, and arguably so until the 1930s, but we should keep that debate in the "historical continuity" thread (where I've just made a long new post!). By election, I'd say in 1904 Teddy was to the left of Parker and in 1924 both candidates were so conservative it was hard to tell, so I'd choose one of those two.
William Jennings Bryan, noted conservative
William McKinley, noted liberal