Monmouth University in a poll found that most Americans, of both political parties, believe that “Deep State” exists and works against the public.
Public Troubled by ‘Deep State’ | Monmouth University Polling Institute | Monmouth University
I think a lot of it may be rooted in shifts in culture, both in government and politics, around the time of the Cold War. There was more intense government secrecy, along with escalating paranoid obsessive rhetoric about all the supposed "threats" facing America, both around the world and within America itself. Revelations about McCarthyism and J. Edgar Hoover's antics helped to feed these attitudes, along with concerns over what the CIA might have been involved in.
Then there was the JFK Assassination, which became a popular topic for conspiracy theorists since the Warren Report was viewed as incredibly implausible. Since the public believed the government was lying, it led to the idea that they must be hiding something from the public (which they were, since so many files and pieces of evidence were marked "classified" and inaccessible to the general public).
Up until that point, our own government was the biggest purveyor of conspiracy theories and paranoid perceptions about the outside world and the American public itself. Naturally, some of this started to rub off on the body politic and it would soon become a noticeable part of our political culture.
The Vietnam War started escalating and the public wanted answers, but the government's answers were not satisfactory. Perceptions of the Civil Rights Movement also came into play, as it was revealed that there were government operations to try to thwart Civil Rights, particularly focusing on surveillance on Martin Luther King. There are still those who believe that MLK's Assassination was a government plot. COINTELPRO became known to the public.
Then there was Watergate, which also fed into public perceptions about government conspiracies. Concurrently, the public was becoming more aware of the existence of the Mafia and organized crime. By the 1970s, it would seem that public cynicism about the government and belief in conspiracy theories might have been at their peak. Most of the public believed that the JFK Assassination was a conspiracy (echoed by a 1978 Congressional Report on it). The notion that UFOs exist and being actively covered up by the government was also quite prevalent and widely believed.
Then there were government denials that the public did not really believe, such as the denials about Agent Orange and the effects it had on those who served in Vietnam. Another typical example might be the government's denial that we had anything to do with the 1973 coup in Chile, but it would later come out that we
did have a role in that event. The public also started hearing more about private organizations like the Bilderberg Group, the Trilateral Commission, the Council on Foreign Relations and other such unelected bodies where the top leaders and movers-and-shakers in society would meet and hold conferences, yet the public was not allowed to know what they talked about.
So, a long track record of lies, denials, intense state secrecy, coupled with scads of delusional propaganda about "enemies" of America both from within and without - all of this had a role in shaping public attitudes and perceptions regarding the government and the existence of the Deep State. Ultimately, the government and ruling class were the ones primarily responsible for creating the political culture which led to such attitudes.
Personally, I have no real stake in any conspiracy theories, although from the standpoint of realpolitik, anything that makes government look bad or undermines the public's faith in government is ultimately a good thing. I believe that if enough public support pushed for it, the government may eventually end their culture of secrecy and become more transparent. I believe that's for the greater good, even if the conspiracy theories turn out to be false.
For similar reasons, I find myself extremely mistrustful of those who seemingly go out of their way to defend the government and attempt to "debunk" these conspiracy theories. Why would they care so much about the government's reputation?
I think about this every time I see a heated discussion about JFK or 9/11. I'm somewhat agnostic about government conspiracies regarding these events. Maybe they happened, maybe they didn't, but there are those out there who have ostensibly made it their life's work to try to convince people that the government is clean, while denigrating conspiracy theorists as "nutjobs" and "loons." But their zeal and emotionalism is what gives them away, since they seem so angry at conspiracy theorists for daring to question the government's reputation. I'll admit that this has always been a mystery to me, since I see no rational justification for such passionate attitudes in defense of our government (unless they either work for government or a paid shill).
On a JFK board I used to frequent, I would encounter these types and directly challenge them: "What's your deal here? Why do you care so much about defending the government?" Even if they truly believed that JFK conspiracy theories were a pack of lies and that Oliver Stone was a "nutjob," why do they care so much? What is their motivation? None of them ever really wanted to give any kind of plausible answer.