What material is used to make capes and cloth in LEGO sets and where do I get it? It seems like a conspiracy to keep everyone from knowing this. 

Custom cape sellers don´t say what it is, the women from the draperies I questioned always say something along the line of "coated propylene" which is no longer in the making because the only company who sold it went bankrupt in 2003. 

Even LEGOs customer service can only say "Acrylic matte medium" which apparently is some kind of paint artists use to paint on canvas.
The term acrylic is used for many mediums, like acrylic paint (liquid), acrylic fiber (clothing), acrylic rubber (flexible) and acrylic glass (really hard).

So, as you see, it is possible to make those capes out of a type of acrylic material.