This is extremely uncommon.

For example, I used to be a submarine officer in the Navy, and I left as a conscientious objector because of this realization. In an average year, less than 100 active duty service members will apply for conscientious objector status (there are over 1 million active duty personnel). If you take a look at [this graph](http://izbicki.me/blog/most-conscientious-objectors-are-not-...) based on GAO data, you'll see that the number of conscientious objector applications dropped significantly after September 11th. This is despite the fact that the wars afterward have been much more controversial and less just.

Why is [NSA moral] low?

I'd bet it's not because of any ethical conflicts. Instead, it's because 100s of man-years of work is going out the window. One of their own betrayed them. This would be demoralizing even for the most ethically unquestionable teams.