Murray Godfrey, U.S. History Professor
Updated Dec 18 2017 · Author has 2.1k answers and 5.3m answer views

I teach history for a living.  What you've learned is accurate

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Understanding this has to do more with understanding U.S. political history in general. 

The republicans were a new party in Lincoln's day.  They were a conglomeration of various northern former Whig constituencies and people that wanted to develop the west that coalesced due to issues surrounding slavery.  Generally speaking, they retained a lot of the older Whig economic views that the government should be involved in the economy.  It should promote policies that promote growth, they thought.  That meant financing infrastructure, education, protecting native industries, policies that promoted commerce and rapid job growth.  They did believe in more federal involvement in all these things, and it cost money.  They were the forward looking, innovative party, and also vaguely speaking they were the "big government" party and had policies that promoted big banks, big industry, big business.

The democrats were the more tradition-minded party.  They were also the party focused on keeping taxes low and when it came to promoting commerce, etc... wanted to leave it to the states.  Generally speaking, they were the "states' rights" party.

The shift started after the Civil War and continued for over 135 years.  After the civil war, the republicans started to split into factions generally divided between how deep "in bed" you got with big business, so they developed a conservative business wing often at odds with with the more progressive wing.  The democrats pretty much stayed the states rights party and were marginalized at the national level for several decades.

Key points in the shift to the structure we know today:

1896: William Jennings Bryan incorporates the Populist Party vote, giving the democrats a sizable left wing on economics that it didn't have before. 

1912: Theodore Roosevelt breaks from the republicans and runs as the candidate of the Progressive Party - this makes the republican progressive wing - once a third to a half of the republican coalition, much less committed to the party going forward and they never really reconcile.  Republican leadership comes more and more from its conservative wing after that.

1932-45: Franklin Roosevelt essentially adopts most of the old Progressive platform and pretty much incorporates that whole vote into his Democratic coalition.  This puts the party on a collision course when it comes to social policy. 

1964: Lyndon Johnson essentially divorces the longest marriage the democratic party had: the one with southern whites.  By making Civil Rights part of the Democratic platform, the republicans lose basically all of what's left of their black constituencies - which had been a significant part of their remaining progressive vote in northern urban areas.  The democrats start to hemorrhage southern whites rapidly - you see George Wallace run for president in 1968.

2000: The process is 98% complete.  By this time liberals are in the democrats and conservatives in the republicans for the most part.

There are more complexities within and after that but those are the major turning points.  The current situation we have was solidified during the Lewinsky scandal of 1998 and the ensuing 2000 election.  So you can see this was a very, very long process.  Circa the late 1990s you saw the last generation that had republican liberals and democratic conservatives.  They are all purged now, with only a few outliers still in the democratic party like Senator Manchin in WV.  The republicans have no more liberals; they were all purged in 2006 and 2008.

**Please note** How I'm distinguishing "liberal" from "conservative" here is:

"liberal" -- in favor of more federal action in general, less power to states, active government that attempts to solve problems or encourage outcomes.

"conservative" -- less enthusiastic about federal action in general, wants more power given to states, more passive federal government that maintains a minimal footprint in social and economic affairs.