These are my feelings on things like this: considering the re-enlisting bonuses they get, I'd say, "Choose your battles." My son in law used to get many thousands of dollars to re-enlist in the Navy. He was not religious at all: he just said his vow and then moved on with his life.
Long before I was a JW, I stopped saying the pledge to the flag. I was in high school. My decision had nothing to do with the "under God" part. My decision was because of the "with liberty and justice for all" part. I felt like until the day came that there really was liberty and justice for all, I wasn't going to say the pledge. I was the closest I've ever been to being an atheist at the time. The god part didn't ever cross my mind. I remember that another guy in my homeroom class didn't say the pledge for religious reasons. I respected his reasons. Danged if I didn't find him sitting at the KH, the first time I went to a meeting.