The consensus seems to be that the Deep State concept is little more than the anthropomorphising of the simple observations that:
-No-one can be an expert in everything so we have to turn to genuine experts when we need to, and those experts bring baggage.
-The civil service has a certain level of intertia and an historical tendency to self-preservation and empire building.
-That corporate culture within civil service organisations persists past any one administration.
These things may be a feature, not a bug. People who gain positions of power often note how little power they actually have - their decision making is constrained precisely to prevent the corrupt or the thieving or the demagogic to have too much power. A judge is constrained by the law, a President by the need to get others such as the military and treasury to go along with mad plans to invade the UK, etc.
Since the example of Trump has been raised, let me use it as an example. Trump affects not to know about the proper constraints on power, as though by act of will he could build a vast wall along the Mexican border, with (by necessary implication) a vast staff to man it, and the capacity to simply demand that the Mexicans pay. Pushback will come from Treasury, for whom it will be an unproductive uneconomic sinkhole, from foreign countries who point to the counter-productivity of these things historically (looking at you East Germany), the State Department who will point out the problems that will emerge with Mexico and aligned nations, and from Immigration who say it will not work, etc.
If a certain cast of mind wants to call this the Deep State’s overriding the decisions of a popularly elected President, I say that is what the complex array of bureaucrats and power-checks is supposed to do. A bureaucracy that gives frank, fearless and non-partisan advice is what we are supposed to have. None of that means a President is powerless to effect change, it just tops-and-tails the more harebrained ends of the spectrum.
A common trope in the conspiratorial versions of all this is that all the visible participants in the political process are mere cyphers for hidden masters. Not really so. Aside from cases of frank corruption, the politicians typically make their own decisions about whose advice they will seek and whose they will accept, based on their meta-skills at making decisions - deciding Dr Fred is an alarmist, the motivations of Dr Barney to be inappropriately passive, etc. Often, their initial ideas about how to behave are modified once they are fully appraised of the constraints that bind their exercise of power of which they were previously unaware. If Dr Barney’s view prevails in this process, that does not mean that Dr Barney is some sort of Svengali who has inordinate control over the brain of the politician.