Tent campers are allowed to use the same sites as rv campers in most of the state parks in my area. Outdoor showers are also allowed in most of these locations.
Tent campers don't have grey tanks. They dispose of their grey water in areas adjacent to their campsites (using basic common sense of course).
I was a tent camper for 20 years before using a travel trailer. I now trailer camp in some of the same sites I used when I tent camped.
I wash my dishes outside using a small basin and occasionally bring along my portable shower like I have always done (once again using basic common sense).
2016 Micro Lite 25DKS, 2015 F250 6.2l Lariat 4x4 3.73's