I dont think anyone answered the original question. The question was not, should the army provide a level of kashrus that satisfies all its members. The question is:
“Does a soldier who is makpid on a mehadrin hechsher have the right to insist that his comrades also be makpid”
The question is not at the institutional level but at the personal level, IE, in the barracks where for example they share a toaster oven. may one soldier insist his comrades do the same.
I’ll wait for Avik to come back and comment.