The "originalism" argument, as far as the 14th Amendment goes, really comes down to how it was passed. They are of the view that the ratification process was illegitimate because it was pushed through Congress by a majority of radical Republicans and that it forced ex-confederate states to adopt it as requirement for readmission to the Union.
The Court immediately gutted part of it (privileges and immunities clause) in the Slaughterhouse Cases (1873), just in time for the Great Compromise of 1877, where the North abandoned Reconstruction and laid the groundwork for the legality of Jim Crow.
That it was intended explicitly to prevent state-sponsored discrimination is irrelevant in their eyes. The Founders didn't pass it and they'd prefer to roll back to just the first ten, namely because James Madison wrote those ten in George Washington's blood the night before Yorktown. Evidence of this comes courtesy of some Lost Cause fucker with a doctorate from Stonewall Jackson University, who will chime in that it's the only possible interpretation available.
Also, dumb people are dumb and easily manipulated into viewing the 10 Commandments as being somehow directly linked to the first 10 Amendments. This bit is somewhat new to the "mainstream" (if there is such a thing), but it's been kicking around the religious SovCit and libertarian circlejerks for a while now.