Really a couple of issues here.

If you're going to launder them, it needs to be in a separate machine from your regular laundry, not just a separate load, because they will leave residue. Some laundromats in working-class areas have a machine reserved for greasy loads. Or you could find a cheap used washing machine.

The other issue is where all those toxic chemicals go after they've left your rags. That's another reason why we use paper towels. (The heavy duty blue or white shop-towels-in-a-box.) I figure in the landfill they at least *try* to keep liquids from leaching out, rather than intentionally sending those chemicals into the water supply in the laundry.

Maybe if you have a simpatico LBS you could get a group of home mechanics together to "sublet" rags through their shop towel service. Although even there, in the US some regulations were passed a year or two ago that allow towel services to pass a lot more toxics into the water supply, rather than wringing them out.