Non synthetic kit will be much heavier but can perform as well or exceed synthetic materials.

For a quiet non synthetic tent there is the Force Ten Classic STD Mk3 4 Season 2 man tent - Although heavy can be a very comfortable tent being very breathable. I remember these tents from about 25 years ago and they were excellent, giving a very quiet and peaceful nights sleep, but they are in reality just to heavy to carry if carried individually.

http://www.vango.co.uk/products/f10tentsInfo.aspx?productid=12&modelid=16

For quiet clothing, cotton Ventile is very quiet compared to synthetic materials. But there are some reasonably quiet Goretex fabrics made called Goretex Saturn. I have a Berghaus Trek Jacket which is almost as quiet as Ventile.

Tatonka make a range of quieter polycotton Tarps.