As no one has ever bothered to define “the elite” it can mean whatever anyone wants it to mean. In our modern world of populist mindlessness, it means “someone who’s IQ is more than 90 and who maybe knows the name of the ocean near Los Angeles.” The reason the Republican Party can position itself in the minds of foolish ignorant people as being “the Party of the ordinary person” despite 86% of their votes being in favor of legislation that massively favors the rich and hurts everyone else is because, as Bobby Jindal (R) pointed out back in 2017, “we’re the Stupid Party.”
Republican voters are, according to several large-scale (>30,000 respondents) IPSOS/MORI polls over the last 3 years: less intelligent, less informed, less educated, more obese, and more racist than the US average.
So basically “anti-elitist” simply means: “we are (or we pretend to be) brain-dead just like you.”