What made republicans at the time of Lincoln the liberal party? Great question! First off, they were socially progressive, supporting abolition/ voting rights for Black Americans. They also supported social safety nets and equity for former slaves with things like the Freedman’s Bureau. There were some especially radical republicans who supported a wide scale implementation of Sherman’s special field orders No 15 — the “40 acres and a mule” that would be given to Black men.
Aside from social issues, they were fiscally large government (like modern day Dems) and supported some progressive economic policies. For example, the first federal income tax and the first federal PROGRESSIVE income tax (rich are taxed higher) were both under Lincoln. It was also his administration that standardized currency across the states — this large scale economic reform was typical of the Republican platform at the time
When you also add in their support for things like universities (Lincoln’s Morril Act which supported agricultural colleges) and for environmental preservation (Teddy Roosevelt, Grant preserving Yellowstone, etc.) it’s easy to see why the Republican party used to be considered pretty liberal! :)