Here is my experience with Ivory Soap: Quite a few years ago I heard of doing this, and so I decided to try it. I bought Ivory Soap and began to brush. After about three days, I got terrible canker sores in my mouth. I was so miserable and it took a week or so before I cleared it up. I am now afraid of trying any soap.
If you have been brushing with Ivory Soap and you have no problem with it, then it's probably okay.