Turkey red oil cannot be used as a base oil in soaps. It's uses are really where you want to get oils into solution with water (or visa versa). It's a detergent and as such, an emulsifier. It's great in small amounts in bath oils, for example, and is useful to help get fragrance oils and other oils to mix into liquid soaps.
I just bought some to use in bath bombs. It is supposed to disperse oils and help to minimize greasy residue in the tub. I don't think it works well in CP soap.