That recipe looks okay - I prefer the 50% lard version because I find it is creamier.
Out of interest, are you a vegetarian or is it just an "ick" factor of using animal fats in soap? If the latter, you'll probably have more actual animal fat on your skin after eating meat than from using a soap made with animal fats
Edit -
I would also read through at least 10 pages in the recipe feedback, beginner, and lye based sections, looking particularly at anything which mentions recipe in the title. Seeing the many variations on offer with the explanation and reasoning builds up a great picture not only of what a property of a saponified oil is, but how that plays in with others in a whole recipe.
^^^^All of this!
That recipe with 25% Coconut Oil is not going to be pleasant to the skin. Drop that CO down to 20% or even 15%. Add the remainder to the palm oil. And why are you avoiding animal fats? Are you vegetarian, vegan, or have a religious reason?