Post hole diggers. Depending on soil, up to two feet deep hole with vertical sides. A two-footer can last a few days with just a little soil on each use. No animal digging later through a wide, shallow, loose soil, pitiful dinky shovel attempt. Folding camp toilet seat. There's something about the smell of fresh soil that stimulates the process.
Totally exposed for a bonafide outdoor experience, a lap blanket for some coverage, inside a shower tent, or as a friend suggested, a bag over the head for anonymity.
Same for a pump up sprayer shower. Add naked, or swim attire.
Over fifty years ago, some fellow basic trainees didn't poop for over a week due to no privacy commodes. Live and learn.