He should be dishonorably discharged.
Not necessarily true.
Many men have honorably served in wars that they disagreed with.
When a Marine is given an order he is opposed to, the proper course of action for that Marine is a smart "Aye aye, sir," followed by the Marine carrying out the order to the best of his ability.
As Patton said "I won't have a yellow bastard in my army."
Separate issue. There is no room for cowardice in the armed forces.
However, there is plenty of room for individuals whose prudential judgement leads them to believe that a specific military campaign or battle is ill-advised, but who will remain true to their oath of enlistment or commissioning and faithfully carry out the orders of the Commander-in-Chief.
His effort will be half-hearted, no matter what he says.
The military is all-volunteer. I'm of the opinion that if a service person cannot support a military effort, and makes that known, he should be shown the door.
And discharged dishonorably.