Coolidge-Hoover is another comparison. If you go back even further William Harrison-Tyler or Lincoln-Andrew Johnson.
How was Hoover to the right of Coolidge?
And how was Lincoln to the left of Johnson? This board seems to operate under the assumption that defending slavery and/or segregation was an inherently "conservative" thing, fine (though I strongly disagree with that). But Lincoln was fiercely pro-business while Johnson was fiercely anti-elite and fiscally populist. You can't just say "President X used big government, so he's a liberal or President Y used small government, so he's a conservative." Unless we're willing to say that the parties have switched ideologies since the Clinton administration (anyone remember "The era of big government is over"?? Or conversely how much Bush 43 expanded federal power and spent like there was no tomorrow??) then it's pretty irresponsible to suggest they have ever switched, which is what you imply by saying Lincoln --> Johnson was a rightward switch.