All commissioned officers, LDOs and warrant officers in the US armed forces, serve at the pleasure of the President. Exactly like civilians who serve in specific billets inside the executive branch of government.
All uniformed personnel can, and in fact have a sworn obligation, to question unlawful orders. What you've describe, would clearly be an unlawful order. Reporting for duty, deploying to a duty station and the like are not unlawful orders.
Uniformed service personal, however, are forbidden under the UCMJ to question command authority, there's a special word for it call "insubordination", and there a specific Article contained inside the UCMJ that addresses insubordination. What this officer is doing is clearly insubordination, as well as about 10 other violations of specific articles in the UCMJ, and that's just off the top of my head.
This is a mistake for this young officer. A career killer at least, and perhaps even something that will land him in the brig (or stockade more appropriately for him).
So is that a yes or a no to my question?
It isn’t complicated.
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