ANSWER: The EO opinion does not apply to military judges. If you read the EO carefully you will see that the language does not apply to military judges.
Regarding the violation "disobeying a lawful order"-->
Here is your language from the Manual for Courts-Martial:
Inference of lawfulness. An order requiring the performance of a military duty or act may be inferred to be lawful, and it is disobeyed at the peril of the subordinate. This inference does not apply to a patently illegal order, such as one that directs the commission of a crime.
Determination of lawfulness. The lawfulness of an order is a question of law to be determined by the military judge.
Read the EO carefully; it says nothing about the type of work done by military judges. This EO is directed towards lawyers arguing in court and representing the United States (probably any court, anywhere on Earth) and says absolutely nothing about a determination by a military judge.
"No employee of the executive branch acting in their official capacity may advance an interpretation of the law as the position of the United States..."
When the military judge makes a determination it is not the position of the US. That happens when lawyers argue in court. When a judge speaks, it is the law speaking. It is a legal fiction but he does not advance interpretations; he transforms interpretations INTO law. Actually he declares the law. The military judge does not represent the United States or advance its positions.
The only issue may be could a military prosecutor (who now in this scenario represents the US) argue that the order was illegal (against his side). If he felt that way he would convince a Commanding Officer to drop the case in the real world so this would never happen.
What does "bound" mean? Could a military judge go up for courts-martial because he did not follow an interpretation? That is not how law works and that is not how the military works.
Will the military judge allow the accused in a court-martial to argue that the order was unlawful? Maybe. The Manual for Courts-Martial states "A general order or regulation is lawful unless it is contrary to the Constitution, the laws of the United States, or lawful superior orders or for some other reason is beyond the authority of the official issuing it." So the strikes are unlawful because they violate which Article of the Constitution? Which law of the United States? The defendant is going to have to point to some positive, enacted law. Maybe the judge will agree.
As for the accused in your hypothetical case, he would go before the military judge and the judge would never invalidate an order from the President in a courts-martial. Then the accused could potentially appeal. Maybe something interesting could happen at the CAAF.
Regarding the liability of the individual who violated an order, it probably depends on if the accused is an officer or an enlistee (see below). In either case, a Commanding Officer could haul them before a court-martial and maybe a panel would decide the case if the accused chose a panel instead of going before the judge and he was entitled to a panel (read the UCMJ I guess if you want to know if you get a panel to decide your case). The panel does not have to explain their reasoning so they could decide not to find the accused guilty because they don't like the order.
Judge Advocates are military officers. They are commissioned by Congress and serve as officers. They are not a part of the judicial branch and neither are military courts. They are lawyers and must be a member of some jurisdiction's bar. They typically do not practice in that jurisdiction however.
Military courts are called Article I courts. Under Article I, Section 8 of the U.S. Constitution, Congress has the power to raise and support armies; provide and maintain a navy; and provide for organizing and disciplining them. Under this authority, Congress has enacted the Uniform Code of Military Justice (UCMJ).
There is no jury at courts-martial. It is called a panel and there are fewer than 12 individuals typically on that panel. It will be led by an officer, but enlisted people can serve on the panel for an enlisted accused. They do not have to find the individual unanimously guilty; the prosecution only needs 2/3rds to convict.
Today a service member would not be court martialed typically for disobeying an order but may face administrative sanctions from his or her Commanding Officer. In our modern military, they may just be chased out of the military or not receive that next promotion.
Officers and enlisted personnel swear an oath to defend and uphold the Constitution. This is an enlistee's oath:
I, (state name of enlistee), 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).
Clearly you can see that they must obey the orders of the President. If they conflict with the Constitution then they must have a reason grounded in law that may well serve as their defense. This would present a gray area, but many men and women are court martialed in times of war for small infractions, like not being on time to their formation. The book "The Execution of Eddie Slovik" is about an enlistee that was put to death at the end off World War II for disappearing from his regiment to go cook for the Canadians.
Personnel may be able to sue the Secretary of Defense. There is an interesting case during Vietnam but it involved Congress cutting off funding for the bombing campaign in Cambodia and President Nixon continuing despite the enacted law. See Holtzman v. Schlesinger, 361 F.Supp. 553 (E.D. N.Y. 1973)
This is the officer's oath. An officer probably can disobey an order that he believes conflicts with the Constitution as long as their determination is based on the law and accepted interpretations of that law.
I, [name], 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; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God.
As most high-ranking officers fervently want that next promotion, it is unlikely that they will risk their career to disagree with their superiors; but maybe some of them have that courage. If so, they are likely retirement eligible and will go out to pasture (voluntarily or otherwise).
