Fleece and jersey knits are comfy soft and don't fray enough to care with regular cutting/tearing. I have rags in my collection that I brought from my parents' house when I left for college almost 12 years ago--and they weren't new then. Yes, the edges aren't perfectly even, instead of being - they are ~
Terry cloth, especially cheaper, more loosely woven terry cloth, frays horribly. You'd be better off buying new washcloths. That said, old cotton athletic socks work for most things washcloths work for. I consider them my "disposable cloth". If I don't want it in the laundry, I grab one of those and throw it away after use.
Oh, and if you did have a pretty fabric you loved and wanted wipe sized, any friend with a sewing machine and 5 minutes could whip round the edges in a zig zag.