Sharing eye makeup is even more dangerous than sharing lipstick and other makeup. Besides the risk of using the wrong colour (oh no!) you have a huge risk of spreading viruses via your makeup. The most common viral infection of the eye is conjunctivitis (also known as pinkeye), which is extremely contagious. Sharing can also lead to increased risk of warts, cold sores, styes, and bacterial infections.
Mascara, eyeshadow and eyeliner, eyelash curlers, and even Latisse - used to stimulate eyelash growth - can lead to a bad eye infection. Makeup cannot be cleaned of bacteria and viruses from previous use and bacteria are carried from applicators back to the product itself, so using a clean applicator does not decrease the risk. In fact, the items can be contaminated for weeks unless they are cleaned and disinfected. This is why it's a good idea to discard items such as mascara brushes and other eye makeup if you've had infectious conjunctivitis, even if your eyes have cleared up.
The bottom line is: be selfish with your eye makeup!