only if the fabric is enclosed in an acid free packaging of some sort- the cedar will stain/leech onto the fabrics with time.
you can buy acid free storage boxes, or even acid free tissue paper- or line the cedar chest with some suitable product.
you can get clear storage (bags) that are suitable that you could put the fabric in first (like the bags that slide under the bed that hold blankets & sweaters) just don't put fabric against the wood.