There is an inherent danger in applying political labels to the past. It was the Republican Party which elected Lincoln,emancipated the slaves, and then administered government through out Reconstruction. This left the Republicans distinctly unpopular in the south, and the Democratic Party held sway for the next century. While the southern Democrats were quite progressive on some issues, they were nearly paleolithic on most social issue, especially racial equality.
When the Democratic Party became the party of racial equality, southern Democrats fought tooth and nail, but eventually, most of them surrendered and became Republicans.
The labels conservative and liberal did not have the same meaning we understand today. The division was mainly over economics. A pre-Civil War Liberal was likely to be in favor of Federal government tax revenues being spent on infrastructure such as canals, roads, and bridges, while a conservative was likely to oppose use of Federal funds, on the grounds that anything which couldn't be built by private investors, did not need to be built.
The social issues which divide today's liberals and conservatives, gay rights, abortion, prayer in school, etc, simply did not exist at that time.