I wash mine in the washing machine with towels, and if it needs bleaching I bleach it. I don’t bleach it very often though. Every time I make cheese, I boil the cheese cloth. I take it out of the boiling water right before I put it in the mold so that it is as clean as I can get it.
I always sanitize mine in bleach. It removes the stains from the annatto coloring as well as any bacteria that might be present. As far as “infusing with chemical cleaners,” the chlorine in the bleach, which is the active ingredient, readily evaporates.