It's the bacteria that builds up that sours the towels, after use you can eleminate some of this problem is you rotate your towels and allow them to dry in direct sunlight before reuse. Reusing a damp towel is more of a culprit than the well-water. Bacteria generally need a moist environment to breed.
I don't know how well this would work with towels or rags but I use sponges and after I use it, I stick it the microwave for 2 minutes. Dries it up and kills bacteria. Then I can get quite a few more uses out of 1 sponge. Might wanna make the switch to sponges or at least invest in a few.