I believe Mac wants to stay away from using palm oil, (is that still right Mac?) Perhaps someone might suggest an alternative to some of the high amount of coconut? I'm not sure myself as I'm still learning about the properties of different oils and butters.
That is a great question.
Oils that are less than clear and liquid at room temperature are that way because of their saturated fat content. There are however different types of saturated fat.
The type of saturated fat in coconut oil or PKO turns into a bubbly, cleansing soap that can also dry or irritate the skin. You want to have it but not too much. Palm oil has the other type of saturated fat that contributes hardness and some creamy lather without such strong detergency. You need both types for a balanced recipe or you'll be stuck making mainly olive oil soaps.
The most direct alternative to palm oil is animal fats. They are in the same category as palm oil despite the very different source. However, some people also prefer to avoid animal fats. So now we've eliminated all the most used soaping oils in this category.
To get more technical for a moment, the category we are talking about with palm oil or lard/tallow is oils with saturated fat composed of a high proportion of palmitic acid and/or stearic acid.
When you eliminate the main palmitic and stearic oils, what do you turn to? The answer is tropical butters (shea butter or cocoa butter, for instance) and hydrogenated vegetable oils. For the latter, some people use vegetable shortening from the supermarket, but the best option is flaked soy shortening. It doesn't have a palm component and doesn't contain as much polyunsaturated oil that can go rancid. Some of it is also sold for candlemaking.