The old Republican party believed that a specific power should belong to each individual state. The Republican party believed that each state had a choice of which religions could or could not be practiced within that states borders.
As the US' Reconstruction period began Radical Republicans believed that freed slaves should have freedom, and the same rights as any white citizen. Other people in the Democratic Party and citizens with no party affiliation also agreed with the Republicans.
In the early part of the political party, the Democratic party did not support the creation the National Bank. The Democrats believed in states rights and wanted to make sure that the country stuck to the Constitution as much as possible.