The problem with the GOP argument is that it is disingenuous. Back then the Democrats were the conservatives and the Republicans were the liberals. The Democrats wanted a small, limited federal government, while the Republicans wanted a larger, more powerful federal government. The Democrats wanted lower tariffs, while the Republicans favored higher tariffs. On most issues, the antebellum and Jim Crow Democrats were the ideological ancestors of modern conservative Republicans, and the antebellum and anti-Jim Crow Republicans were the ideological ancestors of modern Democrats.
Simply put, back then most conservatives either supported slavery and wanted to expand it or at least opposed any efforts to abolish slavery, while most liberals opposed slavery and favored the abolition of slavery or at least favored strictly limiting it to the states where it was already legal, opposed any extension of slavery into the territories, and supported personal liberty laws that prevented slave catchers from apprehending runaway slaves in Northern states that had such laws.