The controversy over charedim not serving in the IDF has always been quietly brewing in Israel, but right now it is more heated than ever. Non-charedim do not see why an entire community should be exempt from the difficult burden that is placed upon everyone else. Charedim, behind the bluster of ridiculous claims about Torah being destroyed (as if there is no Torah learning without 18-21 year old charedim!), understandably fear their way of life being seriously changed. Any form of compromise appears impossible; it's just going to be a battle.
I'd like to propose a plan. It's something that would still be seen as innately unfair by those who do not believe that charedim learning Torah contributes to Israel's national welfare, but at least they ought to see the value in reaching a mutually acceptable compromise. And it's something that ought to be acceptable to charedim. The reason is that it is the approach of the father of the yeshivah world, Rabbi Naftali Tzvi Yehudah Berlin of Volozhin, otherwise known as the Netziv. (I would like to thank Binyomin Eckstein for directing me to these sources in a comment thread at Cross-Currents.)
The Netziv operates from a value system that is as charedi as you can get. In She'er Yisrael 11, he states that Torah is the main weapon of the Jewish people in defending itself against its enemies. He simultaneously notes that those who support Torah study have a share in such defense. And in Haamek Davar to Bereishis 49:14, he notes that the tribe of Yissacher were not suited to war, and studied Torah instead - until David HaMelech forcibly drafted them!
Apparently, then, under certain circumstances, even those learning Torah and defending the Jewish People in that way are nevertheless supposed to be drafter for actual combat. However, what is even more interesting is Netziv's description (in Haamek Davar to Bereishis 49:15) of what happens in other circumstances, when those learning Torah are not drafted. He states that they pay higher monetary taxes to support the military! And he states that they are to be available for whatever purposes the nation requires (i.e. some sort of national service). Furthermore, in Haamek Davar to Devarim 33:18 he notes that they must actually accompany the soldiers to study Torah and pray at the front line (presumably either because the protective force of Torah is geographically concentrated, or in order to boost the morale of the soldiers).
This raises a fascinating question. Since the Netziv believed that learning Torah provides the primary protection, why did he say that Yissacher has to pay extra military taxes and perform national service? I don't know the answer. But perhaps it was because he recognized that you can't claim to be sharing the burden when you're not putting yourself out in a way that meaningfully matches the sacrifices made by others. (This is a point that Rav Mattisyahu Solomon of Lakewood apparently missed, when he claimed this week that yeshivah students not only share the burden equally, but even give more than others. It showed an appalling insensitivity to the sacrifices made by those who serve in the IDF and send their children to be drafted.)
So, here is the Netziv's IDF Plan: Charedim who learn Torah are exempt from serving in the army, but they must pay higher taxes and perform national service, and they must send Torah Study Brigades to the front lines, instead of fleeing during war. I think that it is stating the obvious to point out that this is not what charedim do, it's not what they want to do, and it would not be acceptable to them. But why not, if it is proposed by the Netziv as being The Torah Way? (I think that the answer to that is also obvious, but I'll leave it to others to spell it out.)