DoD civilian employees may be authorized access to U.S. Military Campgrounds and RV Parks.

You can read about who is authorized patronage of MWR facilities in this ARTICLE. This article includes copies of the applicable regulations from the DoD and all of the services. Reading these regulations, you'll see that "Both APF, NAF, and retired DoD civilians" ARE authorized LIMITED use of MWR facilities.

Basically, this means it's up to the local installation commander to allow or disallow retired DoD civilians use of "their" campground. They can even determine to allow DoD civilians still employed, but not retired DoD civilians. This decision is "supposed" to be based upon the determination of local facilities availability and current usage. It's also been known that the local installation commander's policy can change often. If a campground is getting full, DoD civilians may be temporarily denied access to the campgound.

When looking at the camnpground's information on this website, there's a category for "Authorized Users". If DoD are authorized for that campground, it will be identified in this category. However, for all DoD civilians, it would be prudent to call the military campgound(s) you're interested in directly to determine their current policy.