The Republican platform of 1856 was pretty progressive to a modern eye. It called for an end to violence in Kansas and admission as a free state, called for construction of a railroad to the Pacific, endorsed the Constitutionality of Federal Government involvement in building ports and harbors, and opposed calls for the forcible annexation of Cuba.
But it's more complicated than that. The Democratic Platform of the same year condemned Federalism, asserted "That the Constitution does not confer upon the General Government the power to commence and carry on a general system of internal improvements," opposed a national bank, and opposed any Federal measures that would benefit any specific region or industry. Their recipe for access to the Pacific was for a system of post and military roads. Just imagine shipping something from China to California by sailing ship, then by wagon to the Mississippi.
Reading between the lines, the Republican platform favored urban, financial, industrial and commercial interests, while the Democratic platform appealed to rural and agrarian mistrust of banks and commercial interests. In theory it sounds populist, in reality it favored the rural aristocracy, and especially the slave owning interests of the South. Southerners opposed "internal improvements," which would improve mostly the infrastructure of the already technologically superior North. Northerners naturally opposed slavery, not just on moral grounds, but because slave-produced Southern products could undercut northern ones. So the real, built-in conflict was that the party of rural agrarian interests was also the party of slavery.
The roots of the problem go back to the clash between Alexander Hamilton and Thomas Jefferson. Hamilton wanted America to be an industrial and economic power. Jefferson pictured America as a nation of small yeoman farmers, which he believed would result in a more virtuous society. (Despite his genius in many respects, on some things Jefferson could be a nut, and the things he wrote on this subject are just appalling (1). And Hamilton did more to make America what it is today than many of the other Founding Fathers. It's sad that so many people wanted to replace him on our currency. Fortunately, he became a hot property once his musical came out.)
So one group wanted investment in infrastructure and industry, and they represented urban trade and financial interests. The other tended to represent rural and agrarian interests. Which, in the South, represented slavery. So it's a confluence of historical accidents that the party of the elite and socially conservative also represented economic progress, and the party of the rural farmers and those opposed to economic elites also represented slavery.
After the Civil War, America really had a four-party system. Two parties on each side formed unstable coalitions that were, in name, a single party, but really consisted of two very different groups. The Republican coalition consisted of newly freed blacks and patrician Northern whites. The Democratic coalition consisted of Northern urban immigrants and laborers, and embittered Southern whites. Mostly the Democrats attracted those groups who supported anyone but the Republicans.
In the 1884 Presidential election, which pitted Democrat James G. Blaine against Republican Grover Cleveland, we can see the patrician attitude of the Republicans emerging. The Republicans blasted the Democrats as the party of "Rum, Romanism and Rebellion." Rum represented uncouth lower-class vice, Romanism reflected disdain for Catholic immigrants and the working class, and Rebellion sent the message that Democrats disregarded the law and were of dubious loyalty. Indeed, for years after the Civil War, the Republicans labeled the Democrats with the "rebellion" tag. The last campaign platform reference to rebellion was in the 1880 Republican platform. Here we already can see the embryonic shape of the future Right.
As long as the Federal government stuck to fiscal policy and national defense, and left social policy at the local level, this hybrid system could persist. Thus, William Jennings Bryan, of Scopes Trial infamy, actually ran for President three times (1896, 1900 and 1908) as a liberal Democrat. In 1896 he supported Free Silver. It's hard to believe nowadays, but there was once a raging debate over whether a little inflation might be a good thing. Bryan's shining historic moment was his speech where he asked "shall we crucify mankind on a cross of gold?" Silver coinage and mild inflation would have benefited workers and farmers, as opposed to the gold standard favored by the robber barons who wanted their money to increase in value (deflation). In 1900 he opposed imperialism and in 1908 he endorsed trust-busting. Late in his life he supported Prohibition and opposed evolution, leading to his role in the Scopes Trial. However, he was concerned about social justice and was definitely not the sour misanthrope caricatured in Inherit the Wind, which is great drama but very poor history. When Clarence Darrow grilled Bryan on the stand (a tactic that would lead to disbarment today), even many supporters of evolution, remembering Bryan's crusading days with respect, thought Darrow had crossed the line. So in the early 20th Century, it was entirely possible for someone to be an economic progressive and a social conservative, even reactionary. To consider another example, otherwise liberal Woodrow Wilson spoke favorably of the film Birth of a Nation.
At the local level, reactionaries pretty much ruled. Censorship was widespread. The First Amendment says only that Congress shall not abridge free speech. It was not until 1925 that the Supreme Court ruled that freedom of speech applied in the States, by virtue of the 14th Amendment statement that the Constitution applied within the States. This doctrine, the Incorporation Doctrine, has been applied piecemeal as cases arose and has still not been applied to every provision in the Bill of Rights. The term "banned in Boston" reflects the active censorship the city once practiced. (The reason the Incorporation Doctrine isn't universal is that court cases can only be brought over actual issues, not hypothetical ones. So until there's an issue, the doctrine isn't applied.)
It was a great time for white males. It was possible to kill a black man or rape a black woman with near total impunity over most of the country. Discrimination against minorities and women was widespread, open, and legal. For women, career paths were mostly limited to housewife, teacher, nurse, telephone operator or secretary. As long as the Bill of Rights applied only Federally, it was perfectly possible to support segregation at the local level and vote for an economic progressive who supported trust-busting at the Federal level.
The first great shock to the unstable coalition system was the Katrina of its day: the great Mississippi River flood of 1927. The flood killed 246 people in seven states and inundated a seventh of Arkansas at its peak. Black victims were subject to severe discrimination. They were rescued last, were frequently pressed into forced labor, and conditions in black refugee camps were deplorable. One outcome was that the Great Migration of blacks to the north, then mostly stalled, resumed. Herbert Hoover, then Secretary of Commerce, already had a reputation as a humanitarian. He promised to do something about the treatment of blacks, but after he was elected President, failed to push reforms (in fairness, little more than six months into his term, he had the Great Depression to cope with). In 1932 many formerly Republican blacks switched their allegiance to Franklin D. Roosevelt and the Democrats, and stayed there.
The New Deal started to erode the Democratic coalition. Southern Democrats found themselves agreeing with Republicans in rejecting deficit spending and the birth of a social safety net. New Deal reforms would inexorably extend tendrils into many areas formerly subject only to local control. After World War II, Harry Truman's desegregation of the Armed Forces and other civil rights initiatives further alienated Southern Democrats, to the point where Strom Thurmond ran as an independent candidate for President in 1948. The Supreme Court ban on school segregation in 1954 came during a Republican administration, but further mobilized social reactionaries (Both Eisenhower and Thomas E. Dewey, who lost to Truman in 1948, were progressive Republicans). The great tectonic shift came in 1964, when Barry Goldwater (who was a strong conservative but hardly a reactionary, especially by present standards) opposed the Civil Rights Act of 1964 and carried the South, but failed to win the Presidency. Lyndon Johnson continued to push through civil rights legislation, presciently noting it would lose the South for Democrats for a generation.
The Cold War also began to mold a coalition of the Right. Communism's seizure of private property and creation of a state economy appalled economic conservatives, and their suppression of religion appalled religious conservatives. Joe McCarthy tapped into the paranoia and helped create the suspicion that progressives and social activists, if not actually Communists themselves, were dupes at best and sympathizers at worst. And the McCarthy Era strengthened the idea that, whether or not progressives were Communists, it scarcely made any difference because many of their goals were those most abhorrent to economic and social conservatives.
The day they pushed the red button and launched the nuclear arsenal was June 25, 1962. That was the day the Supreme Court ruled official prayer in school was unconstitutional (unofficial and personal prayer is not and never has been in question). To the far right, this was the day the courts "kicked God out of the schools." It was effectively a declaration of war, an unforgivable repudiation of the notion that America was essentially Christian. Any chance opponents of the ruling would align with progressives was totally demolished. (Compared to this ruling, Roe v. Wade merely "made the rubble bounce.")
It's very hard to be a social reactionary and an economic progressive. In the 19th century, when the two spheres were widely separate, it was possible, but once progressive social policy began to impinge on economic policy, tensions arose. If you support labor unions or oppose discrimination, that's very hard to square with a belief in the absolute sanctity of private property. What do you do about poverty? Do you try to eliminate it out of progressive ideals, or tolerate it on the grounds that it's the outcome of bad personal choices? Do you support women in the labor force, or keep them subservient? It's also hard to be a social progressive and an economic reactionary. How can you support eliminating poverty but not support a minimum wage or safety net? How can you favor equality of housing and hiring when there's widespread obstruction of it in the private sector?
Many observers ask today how social and economic reactionaries coalesced. The answer is that social and economic progressives coalesced, and squeezed the reactionaries out. Although there are economic reactionaries who care only about their bottom line and don't give a fig for gay rights or abortion, and there are social conservatives who despise Wall Street only just less than gays or abortion, the reality is there's a substantial overlap between the two groups.
Understanding how the two branches of the Right came together might help understanding the frustrating problem of social conservatives who side with economic conservatives. Many social conservatives would welcome universal medical care, a strong jobs plan, and curbs on Wall Street. But not at the price of helping to enact a social agenda that many of them find anathema.
So yes, the Republicans did oppose slavery and the Democrats did support the KKK. That's about as relevant to politics today as saying you won't shop IKEA because the Vikings once sacked your ancestral village. A more relevant question is this: if there were to be a serious effort to re-establish slavery for non-whites, which party would support it and which would oppose it?
Reference
1. Letter to John Jay, August 23, 1785.
Cultivators of the earth are the most valuable citizens. They are the most vigorous, the most independant, the most virtuous, & they are tied to their country & wedded to it's liberty & interests by the most lasting bonds.
I consider the class of artificers as the panders of vice & the instruments by which the liberties of a country are generally overturned.Letter to James Madison, December 20, 1787:
I think our governments will remain virtuous for many centuries; as long as they are chiefly agricultural; and this will be as long as there shall be vacant lands in any part of America. When they get piled upon one another in large cities, as in Europe, they will become corrupt as in Europe.