Kapok makes fairly good, natural insulation and is extremely hydrophobic, and since it doesn't compress as well as down maybe a stuffed waterproof treated silk "mat" combined with some wool could be decent? As far as tarps, tents, sleeping bag liners etc i wonder about using Tencel? While it's not completely natural, it's still better than a lot of other things. Tencel has three interesting properties which might make it good for something like this.
They already make micro tencel fibers and their resulting yarns and fabrics. If you make the weave tight enough with these micro tencel yarns, then water proof it, it would help and would be significantly lighter weight than the cotton ducks, canvas, etc. Tencel is much stronger than cotton (some say it's almost as strong as polyester, but i don't know if i believe that). Tencel also has "nano fibrils" that form in certain conditions. These are like tiny micro hairs that branch off the main fiber. This can increase insulation some and i would imagine, if you do it right, maybe waterproofing--sort of like creating a WPB type fabric.
Btw, i really like my linen and hemp clothing for warmer weather backpacking. A lot of people don't seem to know it, but both dry much faster and wick much better than cotton, and also insulate better. Hemp is slightly better in that regard because like Linen it is hollow fiber, but it also is porous on the surface of the fiber, so traps a lot of air.
Both are quite strong and durable. For cold weather stuff, i like Alpaca stuff a lot and consider it better than Merino in a lot of aspects. It's true that Sheeps wool CAN be more durable than Alpaca, but only when it's felted to some extent. Alpaca doesn't felt as well as Sheeps wool. Alpaca fibers have a significantly stronger tensile strength than Merino, despite the fibers being semi-hollow--which makes it more insulating per lighter weight, but again if you felt the Sheeps wool well it will end up being more durable than Alpaca.