In our shop used rags get thrown in a metal trash can until the rag cleaning company picks them up and drops off a new batch. They have to be treated as hazardous waste, so I guess the shop pays a significant price to have them washed and the wash water disposed of properly. At home I use paper towels or old T-shirts that I toss out after use.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72