I decided to try an experiment over the last several days. On the theory that back in the old days soap was soap, I attempted to wash my dishes with Ivory Soap.
I tried it using the bar soap. I found that while it lathered and cleaned okay, it left a film on the dishes that was easily seen on glasses even if I put vinegar in the rinse water.
My largest concern was an intestinal one, however. When using the dishes washed in Ivory soap I encountered a case of diarrhea. I am guessing that the film left on the dishes disagreed internally and caused the issue, for when I re-washed the dishes in regular soap the problem disappeared.
Just to be certain it was caused by using Ivory soap on my dishes I tried it again, with the same intestinal results. Since I don’t enjoy diarrhea, I will have to look elsewhere for a more environmentally and frugal alternative to dishwashing liquid, and I cannot recommend the use of Ivory Soap for washing dishes.