“benignuman: What you are saying is not entirely true. There was an article here on YWN just a few months ago about a Kol Isha problem that occurred.
Derech HaMelech,
That story was newsworthy precisely because such things are, b”h, very rare in the modern IDF. The IDF today is the not the IDF of the 50s or the 60s. There is no longer an agenda to “frei out” the soldiers.
Your comparison to women covering their hair is astonishing. We pasken there is a chiyuv for married women to cover their hair. The chiyuv of talmud torah does not require “toraso umnuso” but k’viyas itim. No one is saying that the chareidi soldiers should stop learning, chas v’shalom, it just won’t be their only occupation.
Performing the mitzvah of tzitzis does not come at other Jews expense. Learning full time requires other Jews to pay for your living expenses. Furthermore serving in the army is itself a Mitzvah (arguably many mitzvos).