I’ve been on 10 RS tours. On all of them, at least one hotel has offered some sort of laundry service. Sometimes they list their service on their website. I have also emailed a hotel to ask them about their laundry service if I am pretty sure I will want to do laundry there. These services are not always cheap, but it’s worth it to me. I do sink laundry for small items, but enjoy a service for larger items. I have also used a laundromat on occasion.
The RS guides have always given suggestions about the best options on the tour - which hotel is cheapest, what other services might be nearby, where the laundromats are. If the guide doesn’t offer this information early on the tour (so you can plan), ask them! The guides are all very helpful.
One caution (discovered the hard way) - Some hotels do NOT offer laundry service on Sunday or the weekend.