The washing machines at Disney's Pop Century Resort are standard-type washing machines, so if you just have the type of detergent pods that you throw-in, then I do not see that being an issue.
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You're welcome to bring your own detergent and fabric softener if you have brand preferences. Many guests travel with a few detergent pods and fabric softener sheets in their luggage. Do I need to bring coins for the machines? No, all payment is made via your Key to the World Card (room key).
When it comes to water, you have a bunch of options during your Disney Cruise! You can certainly bring your own bottled water onboard. This must be a carry-on item, and bottles must be factory sealed. Just remember, water is heavy and your room might not be ready for a few hours after boarding so plan accordingly!
Disney Villas with one or more bedrooms have an in-room washer and dryer, along with a complimentary single-use box of laundry detergent. Additional boxes can be purchased through Housekeeping or inside the laundry room for $1 per single-use box.
Most of the WDW hotel gift shops sell Tide to Go pens, usually in the section with the over-the-counter medications. If you just have a small stain, rather than a stinky mess, a quick dab of Tide to Go might solve your problem. Have you done laundry during your Disney vacation?