This is because if you have an open wound in the arm pit and you put deodorant over the wound, the deodorant can get into the blood stream and travel to the kidneys, causing or increasing existing kidney disease. If it says you should not use it with existing kidney disease, then you should not use it.
Deodorants and anti-perspirant contain aluminum. Since aluminum is discarded through the kidneys, if you have kidney disease this could cause a buildup of aluminum in the body. Although we eat, drink and breathe aluminum everyday, it is not likely you will die from the deodorant, but you should consult a doctor before using.