It might have changed but I think retired dod was able to use some campgrounds subject to the local command and only behind just about everyone else like active duty, retire military, etc. I have not checked in years but I seem to recall checking at a couple that said I could stay depending on space available. Now that it can be a pain to get on base someplaces I would only try for the ones off base. There is one by Navy lake at Memphis, Tn. I would try if I couldn't get in the state park nearby or a private park that is nearby.
I got checked by an officer at Kirtland AFB when I was using the snack bar at the bowling alley. My card is a Dept. of the Army retired civillian card and that was sufficient for her. I was told the same thing at the auto hobby shop, space A. No problem at the on base shop-ette but of course not the commisary.