I never did wash those. In fact I got the green ones and they were way too big, so I returned them - they were supposed to be 8-9, but they were more like 10-11. In the past I washed similar slippers in COLD water and they came out fine. If you are afraid that the fuzz will get all over the other laundry, just put them into a zippered pillow case. Good luck!
I haven't wash mine yet, but if you wash in cold water with low agitation from the machine, they should be fine.