If you are going to have an issue with a campsite, it will be the uppity elitist R.V. parks, like the one's that cater to the multimillionaires. Some private sites will have what they call the "10 year rule." These will be the ones most likely to give a skoolie owner grief, especially if it's a redneck coach. Most of the sites with the "10 year rule" will typically only enforce it, if the vehicle is an obvious rolling wreck, and is typically applied to all RV's and conversions, not just skoolies. Since they are privately owned, they have the right to make such decisions.
Public places are under equal access rules, so this is why you'll never get turned away from a public campground short of flagrantly violating campground rules.
So, do your conversion right, make it look super sharp when it's done, and you should have little issue with finding plenty of both private and public places to stay.
1994 Safari Sarengeti Edition 37' diesel pusher
1997 Ford F150
1998 Jeep Cherokee SE 4x4 (toad)
2006 Chevy Aveo LS