My father was a conscientious objector during WW2. His view at the time was that JW's were not neutral enough for him, so he did not join them until some time after the war.
At that time ,WW2, they accepted "re-direction" which more often than not meant working in agriculture, but whatever it was, it contributed to the war effort, if only in an oblique way.
I think the JW attitude is even more liberal now, they certainly would not hold to dad's high standard, and would contribute to the war effort without doubt.
I suppose they have come a little way from urging people to buy war bonds in their literature, as they did under Rutherford, but their position is far from the "neutral" they like to shout about.