In order to be the head of the Army or AF ROTC you have to be a Temple Recommend holder, just like many department heads and Head Coaches.
There are non-lds faculty on staff (sometimes) but I believe that they don't have to abide by the same "HC" as faculty or students (I could certainly be wrong here). At least the some of the non-lds Army NCOs we had appeared to be fine consuming some adult beverages and/or chewing tobacco.
The Poster is an Air Force "cadet" so this certainly doesn't seem to apply to the Army side, if accurate.