Natural toothpastes and dishwashing liquids

I used toothpaste as a substitute for dishwashing liquid for the first time last night and that got me thinking...don't most of us put toothpaste in our mouths at least once a day and rinse it out? And then thinking further...isn't dishwashing liquid made of similiar ingredients as soap?  So shouldn't we also rinse off our dishes well every time or aren't we going to put more soap in our bodies? Or of course we can use natural toothpastes and dishwashing liquids and have less to worry about and here are some of them: David's Toothpaste, With My Toothpaste, and Earthpaste as well as Puracy Natural Liquid Dish Soap and Attitude Baby Bottle And Dishwashing Liquid.