Please read this page: https://guineapigcages.com/location.htm. It should answer all of your parents' questions. Fleece bedding is not only cleaner; it is more economical and looks great! Good luck!
If you have a walmart or target near you, that would be your best bet. You can buy fleece blankets (about 50"x60") for about $5 at walmart, and usually you can find some sort of discount fleece by the yard ($2-7 a yard) there as well. If you can't find it by the yard, I have found that one blanket will do the bottom of a 2x4 with a bit left over (that you can use to make cozies, etc.) If you spend $20 on fleece initially, you should have enough to do 2-3 changes, and it will save you TONS in the long run. It holds up great to washing, just make sure you wash it on your washer's hottest setting BEFORE cutting it to size to avoid unwanted shrinking. I used to spend $30 a month in aspen, and now I just do the laundry and spend 20 mins a day in spot cleaning (vacuuming, sweeping, etc. Not to mention how much tidier it is overall. If you can keep up with the washing, it's so much more economical, tidy, and convenient.