I have several bows that are made from all natural materials, mainehunt. Don't have a sinew string but I do have a couple of strings I've twisted from fibers I stripped from yucca leaves. I've fletched arrows without any glue at all, using feathers I stripped directly from the quill vs bought in a bag. The shafts for those arrows were made from switches cut from dogwood and salt cedar (tamarisk). I made the broadheads for those arrows from bone, fixed into slots in the shafts with pine resin and wrapped in with nettle fibers.
I can make everything I need to go hunting with a bow and arrows using only things I can gather in the woods. I don't shoot that kind of equipment all the time, but I take great satisfaction in having the ability make it. At least I know how to get bows and arrows without having to use a credit card or checkbook.
By the way, I could ride a mule to go hunting, but a pickup has an air conditioner and rides a lot smoother.