I was with the Army under LTC (R) Grawe and LTC(R) Leblow. LTC Leblow and I have a fantastic relationship and I can quote verbatim that in order to hold the PMS position the person has to be a temple recommend holding member of the Church.
And this has been the case from the beginning of the Army ROTC program at BYU by the way, every single one of them has been a temple recommend holding member.
This is also consistent with Notre Dame. I made a great friend from a former ND Cadet who said that their PMS must be a Catholic (although he did not specify whether that person had be actively practicing).
I don't know how it works out, but I just know what I do from the discussions I have had.