A couple of weeks ago, the Economist ran a piece on 'elites'. The writer cautions "Careful writers should avoid this word; it is becoming a junk-bin concept used by different people to mean wildly different things."
It's the same with the phrase 'the establishment'. The Atlantic ran a similar piece to the Economist's saying, "Of course, 'the establishment' has no agreed-upon meaning."
Wikipedia currently defines'the establishment' as, "a dominant group or elite that holds power or authority in a nation or organization." I like the fact that their definition of establishment includes the word 'elite' because now we may be able to agree that both words might be consigned to the junk bin. I can't think many people would self-define as being either part of an elite or 'the establishment' particularly as both words have been flung about wildly as pejoratives in recent politics. But I may be wrong on the self-identification thought.