If you have access to the base, shopping is not the issue. The actual purchase is restricted to personnel that have privileges to do so, thus one would need to present there privilege card in order to Make the purchase,as stated earlier at the exchange and commissary.
You need a military I'D to shop at the exchange but you can make purchases anywhere else without one.
You need a valid military I.D to purchase items inside the exchange, but you can purchase items at stores that's outside of the exchange.
It just takes a military ID card.
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