Here is Rav Moshe’s Psak:
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If you look at this, Rav Moshe says that “one who has a desire to learn Torah and to become a Gadol b’Torah, Hora’a, and Yiras Shomayim has the right (Yesh Lo) to go to Yeshiva Gedola, and there will be a Bracha to Klal Yisrael and a protection to all Jews”.
In other words, this psak is only for one who truly wants to stay in learning – and not carte blanche to all Chareidim to avoid military service. Unfortunately, I know too many “Chareidi” boys who are “in Yeshiva” only because (a) it’s the socially acceptable thing to do; (b) they have no marketable skills. Most of these boys would do much better to go into the army – albeit in a framework designed to meet their religious standards – and get on with their lives.
an Israeli Yid (and proud father of a truly Frum IDF soldier)