Our family has used cloth wipes for nearly a decade. We have several types of fabric as some needs require different textures. Our most common is the wash cloth. I buy a bulk bundle of bathroom washclothes, cut them into four pieces each, hem them. There is a pile that is clothes cut into 8 pieces for those male needs. Why use more than you need?
These sit in stacks on a shelf next to the pot. Hanging on that rack is a spray bottle for each person in the family. It is that persons job to keep their bottle sanitized and full of water. The water is used to make wetwipes, should a person prefer or need a better cleaning than a dry cloth.
We all much prefer this system to toilet paper or store bought disposable wet wipes. We keep a paper roll handy for visitors as we don't want them using our wipes.
It does require some work. Dirty (manure!) wipes go into their own sealed bucket, using a foot pedal. Wets (piss!) go into another one.
These get washed often, usually every few days as I have a rotator washer that is small and takes actual boiling water (something electric washing machines don't use) for washing. They also get a poolshock treatment couple times a month (yeah, I know... the horror!).
I found the commercial washers are too big on the small load, but yours might work. I like boiling water to clean such matters, which household hot water heaters can't provide.
They do take some water. Four gallons for a full start to finish wash-dry routine. Extra one on the poolshock days. Might be able to do with less but for me I find this gives the best results, and given what is on the wipes, I want them CLEAN.
Right now we're traveling for the year so we're back to using 1ply in the RV. I actually miss the cloth wipes.