Vegetables and meats can both be contaminated by pathogens, but differently. Vegetables are grown in dirt and handled by many people. It is therefore common for small amounts of viruses or bacteria to be present on their skin. And a small amount of (for instance) salmonella can cause disease. To avoid this, one should wash vegetables. Neutropenic individuals may need to cook them, but typically they may be eaten raw.

Meats (and beans, and cooked rice) are a different story. They can not only harbor bacteria and parasites, but may also provide an excellent growth medium. Therefore, meat doesn't just have to be washed, it also has to be cooked (unless rigorous precautions are adhered to). It also has to be kept cold because airborne bacteria may begin to grow on the meat and reproduce to dangerous levels. Even small amounts of residue may cause this problem.

So when do you wash your cutting board? If you are a meat eater, the answer should be "every time you cook." If you are a vegetarian, the answer can be "when it starts to look dirty". A bit of old carrot juice on the board just doesn't constitute the same health hazard that a bit of old steak juice would.