I switched to The Muslin Blanket by The Fleece Company. The label says one thing: 100% muslin cotton. No polyester, no fleece, no blends.
Cotton is a plant fibre, so there's no plastic in it to shed. And muslin is woven open, so air moves through it instead of heat getting trapped against you.
It's OEKO-TEX® certified, comes in 13 colours, and gets softer every time you wash it.