The only resemblance today's political parties has to those from 1865 are the names. The philosophies could not be further apart on both sides of the aisle.
IMO ... neither side of the aisle.
Both parties in 1865 would be considered ultra-Conservative, racist and no "Liberal" concerns by any modern political standard.
Progressive ideas, as a viable political platform, were another 30 years away and then by the Republican Party, although Wm Jennings Bryan was a populist of sort and started the Democratic party down the path to where it is today.
The Democratic Party was splintered and in shambles after the presidency of Andrew jackson and did not really coalesce again until the late 1800's. The Democrats never really gained much traction as a political force until The Great Depression although the Republican split in 1912 set the foundation for Democratic part becoming the party of Labor and eventually in the 1930's as the party of social liberalism and government's participation in a mixed economy.
Therefore, I think the earliest time period in which your assertion applies is the 1890's but a stronger assertion is the 1930's with a complete switcheroo by the 1960's.
I agree overall with your point but no party (of any significance) had modern political concerns in 1865.