Many down comforters and;down pillows use a type of woven fabric called cambric cotton. Cambric references the weaving style, in this case, a plain weave. Cambric cotton is typically the most down proof when compared to cotton sateen, damask, or jacquard.
One of the downsides to cambric cotton is that it has an audible crinkle sound. This is natural in new down bedding, but in time, with usage, the amount of audible crinkling will diminish.
Sometimes the fabric is finished in such a way, that between the weave style and the down proof treatment, the crinkling sound can cause concern and distraction for sleepers. This is actually the best fabric for your down bedding to prevent minimal down leakage.
Another similar woven style fabric is a batiste weave, which is basically a cambric style with very fine yarns. This results in in an amazing, almost paper thin fabric. Batiste fabric will have an even more noticeable crinkle sound compared to cambric fabric.
Be assured, that in time with these fabrics the crinkle sound will be reduced not only by usage and washing, but also by your natural skin oils contacting and coating the fabric, to help soften the sound.