Is it okay to wash your hands in the same dishwater that you are using to wash the dishes?  In other words, Can someone use the kitchen sink filled with soapy dishwater to wash hands after using the restroom? Is it safe or just gross? 
No! This risks fecal contamination of the dishes. One of the most common methods for disease to spread is the fecal-oral route. By washing your hands after going to the toilet in the same water as the dishes you're cleaning, you're transferring that fecal contamination to the water and then to all the dishes washed in it, and then to all the food eaten from those dishes. 