How do Shaving Creams, Foams, Soaps ensure cut Hair Fragments that stick & clump between Safety Razor blades are easily washed away? This is my first post on Chemistry SE and I figure it's pretty chemical oriented. 

On Sustainability SE we were trying to find "organic &amp; natural" alternatives which are okay for lubrication &amp; moisturizing (don't really care about foaming etc), but so far we have one key problem: 

Hair fragments clumping and getting stuck in between 3-4 blades of a safety razor and not easily washing out using water, which is not as much an issue with commercial shave products.

Is it some (one or more) active ingredients/chemicals that make it happen or some other chemical phenomenon by which this works?
Active chemicals are called surfactants. It is well explained in colloid chemistry books and kind of in wikipedia (https://en.wikipedia.org/wiki/Surfactant)

And it is possible to find alternatives for such chemicals in nature, but they won't be as effective as artificial.