love dyeing (dying,dieing) stuff.....I use the koolaid method google it and you should find a site explaining dying wool with koolaid works the same for most animal products I have dyed. Though I have only done feathers and deer hair. couldn't find any yellow koolaid though so I have dyed stuff yellow using tumeric.... works but took forever to kill the tumeric smell to my nose 2 hot cycles is a mesh baggie in the wash seemed to work..... I am still not sure if fish can smell the remnants but I don't think so....
For fairly dark hairs I would think you might have to start by bleaching if you wanted a decent dye job..... but I haven't done this.
The deer hair under the fly in this pic are examples of koolaid (and tumeric) dyeing.
As to the actual original questions I don't believe when hair is the topic that animals are bred for tying..... but I'm not sure.....birds are in some cases for sure but animals I think not......
As for organic.... I don't understand the question