Commander, you may not like New. You may not agree with his stand. As his commander, it would be your obligation to punish him according to UCMJ. However, your use of your (delegated) authority to inflict emotional pain above and beyond any required military justice does not, in my estimation, speak to your credit.
I respect New as a patriot. I also respect you, as a senior officer. In this matter, I side with New. Again: what do you do with the Tuskeegee Airmen, and their refusal to follow orders regarding segregation? Bet you would call them heroes. Well I call New a hero. The UN and the US Constitutional are not capable of being harmonized. Care to disprove me, using the Constitution. (Remember, the oath is to defend the Constitution, correct?)
What would I do with the Tuskeegee Airmen. I would listen to their position with courtesy and respect, and then court martial them because regardless of what I felt about a lawful order, it is still a lawful order.