When you buy a military AP, you receive a voucher at Shades of Green. When you go to redeem the voucher at the gate, you are required to show a military ID. We've been asked to show military IDs for all adult tickets. You could probably get away with it for the kids passes, but not for the adult passes.
Now, someone will probably post that they haven't had to show an ID, but we always have, in the 7 years that we've had APs. One time, I forgot my ID, and had to go back to the hotel to get it so that I could activate my AP. This only pertains to the initial exchange of the voucher. I've only been asked to show my military ID 2-3 times when using my pass. Usually because of a problem with the finger reader. HTH!