Popa, there are heterim, for example, if she sings through a micrrophone. Obviously the Army Rabbinate was consulted and it was decided that there is a need which justifies relying on kulot.
What about the fact that you are mevatel an asseh (Rambam Hilchot Melachim 5:1 AND 6:4)? As we all know, an asseh is doche a lo taaseh (if kol isha is d’oraita, which is not clear). Not to mention the fact that the Chofetz Chaim encouraged young Jewish men to join Goyish armies – and asked those who planned to dodge the draft what they would do when we have our owm state and army -even though they would have to do many more issurim.
Cantgetit, Rav Shach gave each person who asked a personal pesak (as with everything else). Once, a very promising bachur felt a strong need to join the IDF (it was during wartime). His rabbanim brought him to Rav Shach and he told them not to “break” the boy. B”H he is still frum. How much more so boys who are not cut out for learning and will at best hang around the coffee machine (in Israeli slang there is even a word for them: parparim – butterflies) or at worst become part of the Shaba Charedi and terrorize their neighbors – as is happening in Mea Shearim.