I really can not see why learning Torah is considered a reason not to serve  in the Israeli Defense Force.  The principle is for a mitzvah that can not be done by someone else, one is supposed to interrupt ones learning. That is from the Yerushalmi Talmud. But even so I can see in times of peace it makes sense. Nowadays this seems more in doubt. at any rate the there are only a few yeshivot here and there [e.g., Ponovitch] that I would consider to be in the category of ''Learning Torah.'' The vast majority are private clubs designed for chit chat. -as is well known.

But I guess it is clear that the issue is never the issue [as Steven Dutch wrote.]] The reason the religious do not serve in the IDF is because  they ask, "Why should we serve donkeys?" (i.e. secular Jews). However, I do not think that reason makes much sense. I have just not been able to see the religious as righteous. (After all, experience counts.)   [The religious world will always deny any and all principles of Torah as long as there is a perceived advantage to their group. Torah is a disguise for them. That is why it is extremely dangerous for baali teshuva to get involved with them because the worth of baali teshuva to them depends only on how much money the frum think they can get out of them or their rich American parents. However i would have to exempt most Litvak yeshivot from the criticism voiced here because is believe their commitment to Torah is complete, not their commitment to their group.

[Rav Nachman of course had great ideas but his teachings are used as conscious traps.]