You can dye sheets made of cotton, nylon, rayon, silk, linen, and wool. However, sheets made of polyester or acetate, or sheets treated to be water-resistant, may not accept the dye well or at all.
Can you dye cotton percale?
As long as it's made of an easily dyeable fiber such as cotton, you should be fine. There is one caveat. Cotton sateen that has been treated to be wrinkle-resistant may not take the dye as well as untreated cotton sateen. It's common for cotton sateen sheets to have wrinkle-resistant treatments.
Can you dye cotton bedding?
Natural fibers—such as cotton, linen, silk, and wool—take dye much better than synthetics do.