We used to have a second machine at my parents house for cleaning the shop rags. Hung them on the clothes line to dry. Machine wore out, parents passed away, sold the house. Here I have a septic system, not too crazy about dumping the shop rag dirty water in the system.
Here is what I use now. 1940's portable electric agitator washing tub, a couple of buckets, the mop bucket and wringer and a couple of hours twice a year. I pre-soak the rags for a week or so in a bucket of Tide. Wash them in a fresh mix of Tide and water, rinse by hand in a bucket of clean water, then rinse in clean water with the agitator. I use the wringer every time, from one cycle to the next. Wring them out real good when done, then pull the clothes line across the shop, hook it on a ring on the wall tighten it with a turnbuckle from Home Depot, and hang the rags over it. I still use the clothes pins my mother used 40 years ago.
Its a little tedious, but not bad. I keep rags sorted, real clean, oil free ones for waxing and polishing the car, and other similar jobs. Another batch is for normal mechanic work. I try to grab a new rag every few minutes so they don't get too dirty. One other batch is ones with large holes in them, badly worn, shredded, oil that won't completely come out, etc. These are my grunge rags for nasty jobs. I continue to wash them, but don't hesitate to toss them when they are done.
Charles