You are going to find innumerable disinfo sites and disinfo thoughts, fear mongering, and attempts by the medical field (to keep you from healing yourself) and the pharmaceutical industry to dissuade you from using MMS. In fact, we have a whole section on the wiki and probably still here on this site of "criticisms of MMS" - This is a typical one where they tell you something that 'might' be a truth, but isn't.
MMS can cause you to dehydrate a bit - this is the primary reason to take the ounce of water per drop dosing. You also will be detoxing from the oxidizing action of the MMS, which will cause you to pee more.
So, could this be a stressor on the kidneys? I would guess that it might if you have kidney disease - but "very bad for the kidneys" - no. However, a good example of using a partial truth to tell a scary lie.