There is a post named State, Army and Religion in the Nafka Mina blog where I offered the following comment:
The separation of religion and state is critical, especially when it comes to enforcement of religious laws on secular people. Yet it's no simple thing when it comes to Judaism which is a "religious civilization" (in the words of M. Kaplan). Israel is the nation-state of the Jewish people and as such it has to reflect the Jewish culture and ethos - otherwise it loses any justification for its existence.
The comparison you make with science is incorrect because of the mixing of fact with value. Modern science is about providing facts about nature, and religion as a system of values provides judgment of what to do in light of these facts[i].
The army on the other hand, is an instrument for executing a policy and it certainly has to reflect a nation’s values. Judaism aspires to encompass the wholeness of life, and therefore everything in Israel or that which concerns the Jewish people has religious significance[ii]. It’s just that we lived in the galut for so long that we have forgotten how it’s supposed to be. The national-religious therefore cannot be indifferent to what goes on in the army. They serve because it’s a mitzvah, and they follow/refuse orders because it’s a mitzvah. The only relevant discussion is what values have precedence over others: the unity of the army or the settlement of the Land of Israel[iii].
[i] A side note: had not Judaism contained a genuine tradition of rationally reconciling Torah and science, religious Jews would have had a problem being scientists. The Haredim in Israel have in fact turned their backs towards those traditions and therefore you can hardly find any of them occupying an R&D post.
[ii] I owe much to the late professor Yeshayahu Leibowitz like appreciating the need for separating religion and state. However, I disagree with him on which issues have religious significance. His determination to refine Jewish faith in the Maimonidean fashion is indeed praiseworthy, but I find his interpretations having an aura of autism …