Unless im totally forgetting something If you're talking complete cloth back abdl nappies you really only have little kings or alphagators from abu (which are the same size but different prints) or animooz from tykables. There's hybrids that are plastic but with a more cloth velcro landing/tape area, they do cut down on the crinkle from the front panel quite a bit leaving the only crinkle is from the rest of the nappy. All of the 3 main north America abdl companies one a version of them, abu, tykalbes (us) and rearz (ca). But getting back on track for full cloth nappies, I'd say that the abu little kings or alphagators are the least bulky out of the 2. They were my go to during the summer when it was super hot and they weren't really noticeable with my shorts (I'm on the smaller size if that matters).
They're biggest downsides though are 1) imo they're tapes are a bit on the weaker side and I've had some peal if I taped too tight, probably do to the glue keeping the velcro part on being too weak or the glue not having good grip on the cloth material. This shouldn't be much of a problem if you have the nappy covered with pants or undies like SparkyDog suggested and are mindfull on how tight you tape.2) Cloth nappies in general aren't the best at odor control but I feel like little kings were worse at it than the tykable annimooz. I was more concerned about having a breathable nappy to deal with the heat and sweat, but idk if I'd use them if I know I'd be around other people and HAD to go just to be certious and aware of any potential smells around others.
Hope this helps at all
Edit: And yeah I'll second what SparkyDog said about people not really paying attention and are really wrapped up in they're own stuff. So as long as you're aren't showing them off on purpose and put the littlest effort in hiding them like wearing a long shirt, I think you're chances of someone noticing or making a deal out of it is smaller than you think.