You may have to start knitting,
For a while, I had a bedside lamp with a very plain beige lampshade, which I dressed up one day with a matchstick / bamboo place setting held together with red thread, so red / bamboo coloured, natural texture. I just wrapped the thing around the shade, cut to size, sewed it up at the back, and had a natural-looking lampshade without reducing the light output significantly.
For the ceiling lights at our place, we gave up and we use either plain exposed pearl bulbs in their sockets (kitchen, corridor) or rice paper lampshades (lounge, bedrooms), which look lovely, suit anything natural and are inexpensive.
"Balloon" lampshade here:
Budget was a huge consideration for us, and we focused on good basics first, and cut out a lot of unnecessary fripperies. We like the resulting simplicity.