In most rule of law democracies the law is above the president. The civil servants are beholden to the law as passed by the representatives of the people, the chief executive can only give orders as allowed by the law. Granted there will be times of murkiness that require interpretation. But "fuck it I'm the president and everything I say is legal" is not a valid interpretation in any democracy I know of.
This is (merely) an argument to roll back the power of the executive branch. It is what it is.
Important to note that USA is a republic, typically in Europe parliamentarianism.
In the USA, both are true. Civil servants can (and should) refuse to follow an order they think is unconstitutional, illegal, or simply unwise. But this won't stop them from being fired for insubordination. I don't think the courts will attempt to force the president to retain subordinates that are actively opposing him on the job.
Generally when you reach that point it ceases to be a democracy.