Pour 1 cup of hot white vinegar and 1/2 cup of hot water in a bowl. Thoroughly mix the hot vinegar and water. Hot white vinegar dissolves detergent residue in washcloth fibers.
Submerge the stiff washcloths in the hot vinegar solution while wearing cleaning gloves. Let the washcloths soak overnight.
Remove the washcloths from the vinegar solution and place them in the washing machine. Set the wash machine to the water temperature setting advised on the washcloths' care labels. Do not add laundry detergent to the wash.
Let the washing machine proceed with the cycles. Add 1 cup of white vinegar (at room temperature) to the rinse cycle.
Remove the washcloths from the washing machine when the cycles are complete. Tumble dry the washcloths in the clothes dryer for enhanced softness.