For those looking for a more detailed description of how the new Republican Party was formed, one can start with a Google search formation of the republican party. One of the items I found was this Salon article Racism and the founding of the GOP: Abraham Lincoln, the Civil War and the real history of the Republican Party.
The political party that grew from these concerns over slavery was the Republican Party. In turn, it nourished and carried forward the public’s anti-slavery feelings. But the party was an amalgam of strangely different elements. It contained men from different political backgrounds, and it combined antislavery convictions and antiblack prejudices.
For any topic as complicated as this is, I wouldn’t expect simple answers. This article can only be expected to provide food for thought, not a definitive answer to many questions. I don’t know if reading the book from which this article was excerpted, Lincoln’s Dilemma: Blair, Sumner, and the Republican Struggle over Racism and Equality in the Civil War Era (A Nation Divided: Studies in the Civil War Era) will provide any more details.