Probably just do commcerial laundries. For most of human history there have been professional clothes launderers. You bag up your clothes at the end of the week, they pick up the bags, wash everything, and send it back to you the next day or whatever. It's been handled at all levels from individual mostly women doing laundry for clients to pretty substantial operations serving large numbers of people at once.
Right now hospitals and hotels have laundry systems with pretty high throughput. It's very doable and largely a solved problem.