this probably is like DOD Civilians. It is up to the local base commander as to who is allowed to use the facilities on his base. Calling the campground direct is probably a good idea. I usually do that even with the campgrounds that don't take reservations. I still call just before going there to make sure they have space available.
A week prior to our going down to Key West the new base CO had decided that DOD Civilians could no longer use the campgrounds. It is well over a hundred mile drive from the mainland part of Florida. As we were checking in there was a very unhappy DOD retiree who was being turned away. A phone call ahead of time would have saved him a long drive back up U.S Highway 1 looking for a place to park.