Is the recipe for my shaving cream complete nonsense? Preamble
I have only basic education in Chemistry (excelled at Organic chemistry nomenclature, but then subsequently quit when I could not grok the simplest replacement reactions). Also I will note I could not find a tag for retail product labelling.

I bought a lot of shaving cream product that I really like. I have been reading the ingredients and I don't understand why it contains so many acids and bases. Perhaps this is an oversimplification, but I was under the impression any acid and base that were mixed would in time, resolve themselves to a salt and an extra water molecule. Let me share with you the ingredients list verbatum so you can see too:


Aqua (water)
Stearic Acid
Myristic Acid
Potassium Hydroxide
Coconut Acid
Glycerin
Triethanolamine
Theobroma Cacao (Cocoa) Seed Butter
Parfum (Fragrance)
Sodium Hydroxide
Melaleuca Alternifolia (Tea Tree) Leaf Oil
Limonene
Linalool


So it seems to me the major ingredients are acids, bases, water and fats blended together with an emulsifier (Glycerin?).

Question
Wouldn't the acids and bases react with each other shortly after mixing, leaving my product with a different mixture of compounds than in the ingredients list?

Speculation
Here is my attempt at answering, so you can an idea that I did put minimum thought into this.


Are some of these things with "acid" in the name, not really acids as I learned them (pH under 7, with a donor H+ ready to go)? And therefore they do not react?
Considering the vendor spells out cocoa butter with a long latin name, maybe they have arranged the ingredients list to impress the customer? For instance writing out Stearic Acid and KOH instead of, say, "lard" or "wax" or whatever unimpressive name is actually the product of the acid-base reaction?
Perhaps the vendor is legally required to print the reagents rather then the product(s), in some circumstances?
Perhaps there is some process in the mixing of the ingredients, or some catalyst that inhibits the reaction? And to what end? For the reaction to happen on my face when water is mixed into the product?
As @Mithoron commented, these are ingredients, not a chemical breakdown of the result.

And, as @Karl commented, traditionally you mix together some rendered fat or oil -- that's a mixture of fats and oils with the fatty acids and glycerin that make them up -- with potassium or sodium hydroxide to make the potassium or sodium salt (conjugate base) of the fatty acids, which is soap.

Here, you've got:


Solvents: 


Water
Limonene

Fats, glycerin, and fatty acids:


Stearic Acid
Myristic Acid
Coconut Acid
Glycerin
Theobroma Cacao (Cocoa) Seed Butter
Melaleuca Alternifolia (Tea Tree) Leaf Oil

Base:


Potassium Hydroxide
Sodium Hydroxide
Triethanolamine

Extra smells


Parfum (Fragrance)
Also Limonene 
Linalool
Also tea tree oil



The only reason it has so many is that they've mixed together either a few different soaps or a few different fats before saponification (soap-becoming), and each soap will have been (mostly) neutralised.

Edit: note that the cocoa butter and tea tree oil are almost certainly added after saponification, for fragrance, to alter the material properties of the product, and to be left on the skin.