Many down comforters and down pillows use a type of woven fabric called cambric (or cambric cotton). Cambric references the weaving style, in this case this is what is considered a plain weave. Cambric cotton is typically the most down proof when compared to cotton sateen, cotton damask, or cotton jacquard.
One of the downsides to cambric cotton is that it gives a very 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. Don't worry, 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 80's (very fine) yarns, resulting in an amazing almost paper-like thin fabric. This batiste fabric will have an even more noticeable crinkle sound compared to the 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.