It does, however, require you to swear or affirm that you will follow the orders of the President, and the UCMJ puts the onus on the accusing service member to prove that an order is unlawful. It’s a lot to ask of service members that likely only joined because they needed college money.

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)."

Edit: Ya’ll are right, I didn’t realize the officer oath excluded the “following orders” bit.

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; 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. (Title 5 U.S. Code 3331, an individual, except the President, elected or appointed to an office of honor or profit in the civil service or uniformed services)