I recently made a bunch of reservations for a trip to California state parks. Many of their sites are "Tent Only." I've also seen this at USFS camps, where tents get the nice shady sites by the stream and RV's are out in the field in the hot sun, not exceptions for small RV's. I was asked by rangers to leave groups I camped with at two California national parks because park policy was absolutely no RV's at group sites; I had to buy a site elsewhere and walk back to the group site to be with my friends.
The other side of the issue is that my tent camping family members are often not allowed to camp with me in the RV sites. Some RV parks do not allow tents at all.
Can't we all just get along?
The issue is apparently not vehicle size, it is vehicle type. The solution of carrying a small tent in your small RV and pitching it at the Tents Only site is apparently not acceptable in these places.
KOA's have let me camp in their tent areas. I cannot remember whether they say Tents Only or whether they are just designated as primitive or no hookup sites.