Curious the claims of JFK being “Conservative.” If he truly was, why did Reagan bolt from supporting the Dems ? The Dems had been taken over by the Socialists way back in 1896 when they purged the sane center-right Cleveland Bourbonites. When the party nominated center-right John W. Davis in 1924, the leftist base lost their minds and bolted to support 3rd party Progressive (leftist Socialist Republican) Bob La Follette, Sr.
The base never let anyone center-right near the Presidential nomination again. They wouldn’t even let centrist VP John Nance Garner have the nomination in 1940 to displace FDR. If JFK had been seen as that, he’d have lost the nomination in 1960 to left winger Sen. Hubert Humphrey.
Though I would say that a few ( VERY FEW ) Dem presidential candidates/presidents, after 1896, weren't quite full on Socialists. Grover Cleveland was the last of the "good" Dem presidents.
Al Smith wasn't all that much of a Socialist ( just a DIRTY TAMMANY HALL one), but also never president.