EricDawg-I wouldn't expect decent-quality cotton, wet with shampoo mix, to mar paint, but I guess that "decent-quality" bit can be tricky.
Back when I used when I used cotton for washing, I used Viking brand chenille mitts. Dunno if you can still find 'em though.
Back before MF became so popular, a guy named
Kevin Overall used to buy Charisma towels (medium-high grade supima cotton, not wonderful but not crappy) and cut off the borders. He'd then reserge them with cotton thread. They were pretty nice, and easier to use than "regular" towels because you didn't have to fold 'em up so those serged-with-synthetic thread edges were safely away from the paint.
It's the edges and stitching of "normal" nice towels that will mar the paint. I'd still be careful though, even that cotton serging can mar paint.
Griot's used to sell cotton wash mitts and towels, but IMO they weren't as nice as the Charismas and to be perfectly honest, I consider Charismas to be about the minimum/bottom line when it comes to cotton towels; I use better towels/washcloths than that on my skin, which isn't as delicate as some autopaint
So...you could just buy some nice Egyptian Cotton towels of >600 gramweight and use those. Just be careful about the edges/stitching or cut and reserge them (with cotton thread). There are zillions of textile vendors selling towels like that and I always suspect that the best ones all come from the same manufacturers.