Republicans define “elitism” with cultural signifiers: If you like latte, live on the coasts, eat organic food, drive a car made in northern Europe (Saab, Volvo, VW…) hunt birds rather than deer…etc.
Democrats, back in the days of Harry Truman and FDR, defined elitism in economic terms - “Malefactors of great wealth,” “economic royalists,” “the rich, lolling obscenely in opera boxes…” (actually, that was Mencken).
A reporter asked Sherrod Brown a couple years ago why so many rural and poor whites were voting for Republicans. His response: “Because Democrats stopped talking to them.”
A big piece of that has to do with the Civil and Voting Rights Acts, and their political aftermath. LBJ said that “we’ve lost the South for a generation” due to those Acts, but he lost more than the south: Racist whites everywhere were alienated from the Democratic Party. Part (at this point, only a small part, I hope) of the “elitist” charge is lingering resentment against urban northeastern Democrats for overturning the structures and privileges of Southern Post-Reconstruction society. The “outsiders” who tore down a system that had worked (for whites, anyway) for a hundred years were the original targets of the charge of elitism.
I am far to the left of most democrats these days because I’m an old-fashioned economic liberal - I’d love to see a far more progressive income tax, tilting the playing field in favor of union organizing, government regulation of public goods, single-payer health care, and so on.