As professional as one could be, it would just gradually eat away at anyone knowing they were contributing work to something that they are at aims with.
I recently went through this (not military related) - working on something I had conflicts with. I did it for a few months and then, for the first time in my career, one morning I really did not want to go to work. I sat and stared at the wall for 10 minutes wondering if I should go or not.
Yes but I talked with them and fortunately, they were pretty accommodating. I now work from home (which is something I wanted) and don't have to work on that project.
I recently went through this (not military related) - working on something I had conflicts with. I did it for a few months and then, for the first time in my career, one morning I really did not want to go to work. I sat and stared at the wall for 10 minutes wondering if I should go or not.
This is probably the reason they ask.