iirc rice and potatoes and simply carbohydrate stores?
they might take a bit longer to break down but i imagine, being a source of sugar/energy, the worm bin micro-organisms would do just fine given time.
diary and meat products are ok in bins to a point. a bit of butter in your mashed or chicken stock in some pilaf is minor. just as long as you always allow your bins some wiggle room to adjust to environments that might go bad.
*you might already be aware but from what i know it's the fat in diary and bad bugs in spoiled meat that can cause problems - both for the worms and people. the worms i know are mostly vegetarian but a few bones and shells have been known to turn up in the vc from time to time.*