In those hotels where the "Government Rate" is less (not always true) than the normal spread of rack, regular, and special package rates offered, acting under the theory that the b*stards wouldn't rent rooms for that price unless they wanted to rent rooms, I have, since 1961, carried and used my Active Duty Military, then Military Reserve, now Retired Reserve ID at all times and in all places. Not only does it help get "Gubmint Rates" (when worth getting, it allows me entry into saloons in the far flung, world-wide US defense establishment (and some "furrin ossifers' watering holes" and messes also).
I don't recall in the almost half-century ever being challenged as to the privilege to do so, but have been asked to present the ID on numerous occasions.