An order that violates the U.S. Constitution is not a "lawful order."
Are you familiar with the saying “you may beat the rap but you won’t beat the ride”? It applies here in the same way it applies at the side of the road when attempting to adjudicate a ticket with the traffic cop. Further, by establishing the Uniform Code of Military Justice in the interest of good order and discipline, the Congress determined that the special circumstances of military service required structure not found in the Constitution.
At some point in the appeals process, there may be some finding more aligned to your point of view. However, that won’t be the daily reality of cheerful obedience to the orders of your superior NCO/officer.