When you phone campgrounds do you ask them if it's permissible to bring your vintage camper? Do you ask them if they have an RV age restriction? I ask these questions because other than seeing some comments on this site about certain parks having RV age restrictions I've never witnessed this kind of problem. Our RV isn't new (12 yrs old), but it's well cared for and never experienced a problem. I've also read many RV park websites and other than the occasional park for class A's only I haven't seen any restricted parks.
As stated above, state, federal, or country parks don't care what age or model RV you have. We have friends with a 1974 GMC converted school bus camper and I know they've never had a similar problem. While they usually use state parks, they have used private CGs too.