The restorationists are neither anti-elitist nor anti-intellectual. William F. Buckley famously said that he would rather be governed by the first 2,000 names in the Boston phone book than the Harvard faculty, but few would dispute that the Latin-speaking harpsichord player who used summer and winter as verbs was anything but an elitist. Similarly, the restorationists have any number of hero intellectuals (from Buckley and Thomas Sowell to Hayek and Ayn Rand).
The “elite” the restorationists dislike is better understood as a “new class” (to borrow a phrase from the late Irving Kristol). The legendary economist Joseph Schumpeter predicted in 1942 that capitalism couldn’t survive because capitalist prosperity would feed a new intellectual caste that would declare war on the bourgeois values and institutions that generate prosperity in the first place. When you hear that conservatives are anti-elitist, you should think they’re really anti-new class.