You're misframing this. The conspiracy theory is not that Trump is taking on the deep state; it's the existence of the deep state to begin with.
>If deep state/swamp/etc is interpreted as a vague reference to the Washington/New York professional classes who populate government in huge numbers and tend to share very similar worldviews and beliefs
Speaking of grotesque distortions of the truth, that is not what the "deep state" has ever referred to. It's always been, by definition, a conspiracy theory. It generally posits that the country is actually run by a group o unelected individuals in secret that orchestrate events in this country up to and including the selection of presidents.
The notion that most rules are invented and implemented by the unelected isn't extreme, is it, it's more like an observation of how the system really works, especially in the US where - unusually - regulatory agencies can create new laws without involving Congress.
No,.that belief was a side effect of (1) the fact that it was, to a certain extent true that her nomination was largely a product of elite arrangements and structural advantage, and (2) the deep and broad unpopularity that was the actual reason she ran aground in what should have been the easiest election for Democrats in a long time.