RE "They are, however, bound by their oath and service commitment to continue to follow the orders of their superiors - to see the mission through.":
Upon joining, their primary oath was to uphold/defend the USC. So it's their duty to refuse orders which violate it (that's what "defending it" means).
Those who take part in UNdeclared (and hence UNconstitutional) wars are directly violating their oaths by undermining that which they swore to defend.
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