I'd be interested in seeing what part of the UCMJ supports that. I'm not aware of anything that grants a servicemember the authority to interpret the Constitution.
U.S. Constitution, Article VI ¶2: "This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding."
Unconstitutional orders (or statutes, regulations, ordinances, etc. or other governmental rules or actions) are illegitimate by definition. Any rule would would require a soldier to obey an unconstitutional order is void.
To be sure, there are many cases where reasonable people could disagree whether an order is constitutional; in such cases, a soldier should follow it. On the other hand, there is nothing in the Constitution that gives court rulings any authority whatsoever other than in the specific case at issue, any government action which could not be constitutionally justified without reference to court precedent is constitutionally unjustifiable and illegitimate. It's perfectly proper to use past court decisions to decide whether something is constitutional in those cases which would be truly ambiguous otherwise; it is not legitimate, however, to cite them as primary authority to reach a decision which could not be reached in their absence.
And how do they tell the Constitutional ones from the unconstitutional ones?