In the US, the Democrats are the party of More Government, so the mass of government employees skew Democratic in their voting behavior and policy preferences. Likewise, many of the agencies engaged in certain hot-button areas (e.g., the EPA) deal in causes beloved of progressives, so many of those who go into government service in those agencies tend to have a proggish view of things. This is a perennial problem for Republican administrations, and not just that of Donald Trump. No matter what they were elected to do, the permanent government resists.
Right now, there's a big foo-fa-rah over certain government agencies being stopped from updating blogs and websites until agency heads can be confirmed by Congress and new policies promoted. Various members of the permanent government are attempting to defy the President, casting his attempt to take control of the policy expressions of the government as some kind of dictatorial exercise of power. This is not brave resistance, this is arrogance.
Look at it this way. On the other side of the political divide, the US military in recent decades has tended to skew Republican, since the Republicans have generally favored a more robust defense establishment and the projection of American power. Also, the military is innately conservative in its social structures and values, and Republicans have been more supportive of that than Democrats. In response, both Bill Clinton and Barack Obama cracked down hard on the military to get it to do -- and say -- what they wanted. Obama was particularly ruthless in promoting and demoting military leaders on the basis of the values he wanted his administration to reflect. Careers were ended, careers of honorable and capable officers, because they just couldn't wrap their mouths around what the President wanted them to say as enthusiastically as he demanded it be said.
So, before everybody gets froke out about Trump issuing "gag orders," just stop and breathe. This is not a new problem. Every administration has at least some of this to wade through. And it needs to be said: The responsible government has the right to enact its policies, subject only to the checks and balances in the Constitution. The permanent government just work there. Nobody elected them. They are not part of the checks and balances in the Constitution. They should do their job and quit grandstanding when somebody they don't like is elected.