I recently tried using my olive oil liquid (potassium) soap on a few of my dishes, it worked well! I don't know how it will work cutting grease, but I feel better using it.
Good for the hands too!
Mine is simple. About 1 lb of soap scraps melted in 1 gallon water. Heat to gentle boil, simmer about 10 minutes until everything is melted and then put in jars. It's pretty much old fashioned soap jelly like my great grandma used to make.
Edited to add: This is for hand washing only. I use the borax and washing soda mix in dishwashers.
A 100% coconut oil potassium liquid soap would be wonderful for hand washing, I have used mine. I have hard water so it doesn't suds up too much but it does a great job with the grease cutting.
don't use SOAP in your dishwasher. it's a mess, it leaves horrid mineral deposits in all but the softest of water (think distilled!) and will gum up the works.