Could cover up the end portions of the cabinet with "movie curtains." Use this type of fabric (it is fire proof and is what I made our stage curtains out of).
How to hang? Not sure that tension rods at the top of a shelf section would be strong enough but you could install a shower curtain type of rod. (With the cups at the end). Or do a rod across the entire unit? Sew a rod pocket at the top of the fabric so that it could be pulled to the side to access stuff hiding behind on the shelves. Here's a mock-up:
Not shown: The idea of doing the curtains from the top of the room -- more long term storage behind, on the top shelf!
-- Carol