An “elitist” is a person who assumes that he or she is more capable than the general ruck of humanity whether or not such an assumption is justified. “Elitism” is reliance upon self-declared members of the elite, whether by persons who are thus self-declared or otherwise. People who do not consider themselves members of the elite may be elitists if they are depending on elitist self-declaration as a way to choose leaders or managers.

Now: it is an observed fact, throughout the ages, that people who are in fact highly able tend strongly to be at least somewhat humble about it. People who are genuinely elite have no reason to brag about it or assert it, because their actions are sufficient to establish their status.

A person who loudly claims elite status can be assumed, a priori, to be an individual of ordinary or less ability whose claim is based on something other than performance or capability to perform. That “something” may be a credential of some sort, however obtained, but is more normally based on membership in a group of the self-declared elite.

It follows that “false elitism” and “pseudo-elitism” are oxymoronic. It’s a word definition thing.