Recently, I located an inexpensive vintage alfalfa sack (similar texture of a vintage flour sack, but not as wide). I simply cut it down the middle evenly.
With a hand sewing needle and sewing thread, I put a running stitch through the cut side of the bag. This way, if I decide to cut out the cubbie shelves, and put on actual doors (to store baking sheets, cooling racks and large container lids), I can reuse the sack for another purpose.
I used silver tacks (nice and strong ones) to attach the cut pieces to the cupboard, covering the cubbies. Use a hammer to gently tap the tacks into the wood.
I attached the left side of the bag on the left, and right on the right side, so it gives it character and balances out.
This goes well with another space in the kitchen in which I used an entire bag as a full cupboard curtain.