I first met GEN Milley ten years ago; I think for a 3/4 star level officer he is definitely in the top third in terms of NOT being "woke" on every issue, but at the end of the day he supports his boss or resigns. I will say there are VERY few Army officers who get their 2d star who are actually conservative (quite a few one starts though), maybe one or two per decade. West Point produces the most liberal of all for the Army and it has been that way for twenty years.
What about when the first clause in the Oath of Enlistment conflicts with the latter parts of the oath? I, _____, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; and that I will obey the orders of the President of the United States and the orders of the officers appointed over me, according to regulations and the Uniform Code of Military Justice. So help me God." (Title 10, US Code; Act of 5 May 1960 replacing the wording first adopted in 1789, with amendment effective 5 October 1962).