Avi K:
Can you site to anything where either rav held that “Dina malchusa dina” would require obeying a conscription law aimed at getting yeshiva boys out of the Beis Medrash and into the barrack? The public statements from them and their talmidim suggest it doesn’t.
In any event, Dina Malchusa Dina would usually apply only to laws affecting welfare or safety, but not to laws that are clearly aimed at undermining the learning of Torah. Anti-Jewish laws were never held to be protected by that doctrine.