It doesn't matter what I think. Perhaps if you believe that the CNO represents part of the establishment though in this case, and POTUS believes in his gut that the Chief deserves to retire as a Chief, then so be it, the buck stops with him.
Do I think it is good to be out of synch with the CNO? I don't think a disagreement over a personnel discipline decision equates "out of synch". At least not on a strategic meat and potatoes level.
The reality is POTUS's base don't know who the CNO is. No one outside of the Navy knows or cares who the CNO is.
That's what my reference meant regarding POTUS's desire to appeal to a much larger segment than the minuscule naval officer corps.
The political value here is POTUS sticking up for a career, multi-combat tour, senior enlisted SEAL who made a really dumb decision to take photos with dead people. POTUS decided that the roughly six months pre-trial confinement in the brig was likely sufficient punishment and the lifetime ramifications of a reduction in rank and the humiliation of being a de-frocked Chief wasn't appropriate. Your mention of the perception that POTUS is sticking it to the CNO makes it a two-fer. But I don't think the average schmoe gives two shits who or what a CNO is.
Very few folks outside of the military, really the Navy, are even paying much attention to this beyond the optics of Trump coming to the aid of a SEAL who killed bad guys and got in trouble for....something. The civilian world, which has been said countless times on this board, is utterly and willfully ignorant of the military by design and Trump is really good at taking the oxygen out of a room.
The bullshit about process is just that. Lastly, the fact that career politicians and bureaucrats on both sides of the aisle disdain him, makes POTUS more endearing to a lot of people.