Synthetic motor oil is an admixture of chemically-derived substances, many of which are still petroleum-based.
Baby oil (mineral oil) and vasaline are NOT safe products -- just because something doesn't kill you right away doesn't mean its safe. There is a history of products once sold that have been taken off the market. If you look around, you will find many articles and scientific papers devoted to the dangers of baby oil, vasaline, and other common petroleum-based personal care products. My brother has a PhD in immunology, and he could go on and on about it.
We are all entitled to believe what we wish, but one of the main reasons that I and many others got into making homemade soap is a desire to create a safer product. This concern for the use of safe ingredients is one of the main arguments currently being used to help save our homemade soap industry from being regulated -- like a cosmetic, or a drug. (Check with the HSMG - the Handcrafted Soap Makers Guild) If you made soap using motor oil, synthetic or not -- how would you label it for sale? Using a legally-purchased substance, like motor oil, for a use that it's not intended for is probably illegal if used in personal care products. I apologize if my tone is harsh, but I just can't understand why there is a desire to use a potentially dangerous ingredient.
Okay, I'll get off my soapbox now.