This title is misleading.
Any bureaucracy may help, or hinder, an executive. The term in this case refers to the security bureaucracy, or intelligence community. Various concern trolls are sounding the alarm at the anti-democratic capacities found therein.
The main example used is Turkey, and more recently, Egypt. If the military finds the executive leading the state in a direction they disagree with, cue the coup. The version applied to the U.S. points more at the intelligence agencies.
A recent example of pushback from this community is the runup to Operation Iraqi Freedom, when rank and file were not on board with the conclusions of the neocons. And now we have pushback from the professionals against Trump's dangerous incompetence and likely compromised status.
So the question is: "Are these Deep States a threat?" My feeling is no, so far, as they have in the main pushed back against autocracy, as in Egypt, and a history of that in Turkey has until preserved secular democracy. I think the U.S. version tried in 2003 to prevent the Iraq invasion. And I am not unhappy with the Deep State sounding alarms about Trump.
Is it anti-democratic? I do not get the impression that a small cabal is directing our "Deep State's" actions, rather a general sense of danger and alarm is motivating various separate actions. Similarly, while W was nominally the executive, his team steamrolled the professionals to enforce a view that lacked foundation, basically lying to the public. (I grant that some of the administration types believed their propaganda.) So a "wisdom of the crowd" is at work here, I think, and it is not anti-democratic. It is acting on truth and competence, and not (to my knowledge advancing a self-serving agenda.
So I celebrate our particular Deep State. It consists of both adventurous cowboys and cautious analysts, closet Nazis and dedicated liberal good-government folks. It's ok with me if a situation that calls for drastic action provokes drastic acts. They failed to block W, but many of them served honorably while preserving their standards and the record as well.