People felt angora goat and rabbit hair, but some kinds of hair don't give a very happy result no matter what you do. In other cases, a fiber that won't felt to itself can be blended with sheep wool and then you can get a good result. For example, I know that horse tail hair just doesn't felt well at all -- it's so smooth, wiry, and coarse that it would rather work its way out of a felt than stay put. But horse body hair will felt. Cat and fluffy dog hair will felt, although the smooth, wiry hairs from some dogs won't felt well -- the guard hair from my collie won't felt, but her downy under-hair will. If your goat hair has any kind of wave or curl to it, it may felt okay. The finer it is, the better.
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As far as soap being used to make pills or as medicine itself ... to be honest I don't think that has been much in favor for a long time, but it was done. I know it's not been all that long ago that I read about using soap to make pills, but I can't dredge up the reference. My guess it is in one of the pharmacist formularies I've got and there are always a bazillion references to soap to wade through.
But here are a few tidbits that relate.
First, a recipe for a "physic" meant to be taken internally. It comes from a pharmacist's journal from 1901, but this is the only soap-related item I could find in this journal that was meant to be taken internally. The same journal has tons of recipes that use soap in all sorts of everyday products including shoe polish, harness blacking, floor wax, cold cream, tooth pastes, perfumes, hair pomades, etc. and of course soaps for washing the body. So you can see the idea of soap as internal remedy wasn't too popular any more.
PHYSIC-BALL.
Barbadoes aloes 4 drs. (dram)
Powdered soap 1 dr.
Oil of caraway 15 m. (minim)
Enclose in a capsule.
And here are a couple of old treatises from the 1700s that attribute amazing properties to soap taken as medicine. These examples describe how soap apparently dissolved what I think were kidney stones --
A Letter from Mr. Rob. Lucas, concerning the Relief He Found in the Stone from the Use of Alicant Soap and Lime-Water, to His Brother the Rev. Mr. Richard Lucas F.R.S. 1753.
https://archive.org/details/philtrans06843489
An Account of the Virtues of Soap in Dissolving the Stone, in the Case of the Rev. Mr. Matthew Simson. Communicated by John Pringle, M.D. F.R.S. 1757.
https://archive.org/details/jstor-105252