Besides what the textile is made of, it also matters what they *do* with those fibers. "Microfiber" can be made out of natural or synthetic materials, it's the "micro" nature of how those fibers are used that makes the (functional) difference. Guys like DFTowel have posted some very informative stuff about the textiles we use when detailing, it's more involved than one might think.
I have 100% cotton towels that'll mar automotive paint as if made out of sandpaper, and the diapers I have are among the *worst* in this regard. That's in addition to the "no nap" issue where dirt has nowhere to migrate to away from the paint.