I use exact oils & I don't have to use TD but when I do it does keep the Soap nice white & not an off white after cureI agree that kaolin won't make much difference, but it is nice in soap. Titanium dioxide will make white. My soaps with lard, coconut, (regular, not extra virgin) olive oil, sunflower oil and castor oil is pretty white and I don't use TD. It's not snow white, but is a creamy white.