I would be terrified to use a laundry mat. You never know what the person before you washed and if the machine was cleaned. We have three laundry mats here in town, but we also have two horse racing tracks. Those filthy horse blankets leave the washers unusable. One place does keep everything clean, but I went there to wash some large rugs the washers smelled like diesel fuel. Yes someone washed shop mats (these are heavy pads similar to the pads movers use to wrap furniture when loading into a moving truck, they are used under the truck for the mechanic to freely move around and to also absorb any oil or fuel that may leak during repairs). My husband owns a diesel repair shop, but sends his mats out, cost more, but he refuses to let his trashy mats ruin someone's washers.
I would be so afraid some nasty stuff that may not be noticed in the washer, may ruin a quilt. I hand was my quilts in the bath tub. Great upper body exercise!