It basically depends on type/quality of wool one chooses. Here, Cashmere wool is taken into consideration.

About Cashmere wool:

Cashmere wool, usually simply known as cashmere, is a fiber obtained from Cashmere goats and other types of goat. 

 In the United States, under the U.S. Wool Products Labeling Act of 1939, as amended, (15 Uction 68b (a)(6)), states that a wool or textile product may not be labeled as containing cashmere unless:

    such wool product is the fine (dehaired) undercoat fibers produced by a cashmere goat (Capra hircus laniger); the average diameter of the fiber of such wool product does not exceed 19 microns; and
  • Such wool product does not contain more than 3 percent (by weight) of cashmere fibers with average diameters that exceed 30 microns.
  • The average fiber diameter may be subject to a coefficient of variation around the mean that shall not exceed 24 percent.

Cashmere wool fiber for clothing and other textile articles is obtained from the neck region of Cashmere and other goats. Previously, fine-haired Cashmere goats have been called Capra hircus laniger, and were treated as subspecies of the domestic goat Capra hircus. However, these cashmere goats are now considered a part of the domestic goat subspecies Capra aegagrus hircus. The Cashmere goats are known for the double fleece that they produce, which consists of a fine, soft undercoat or underdown of hair mingled with a straighter and much coarser outer coating of hair called guard hair. For the fine under down to be sold and processed further, it must be de-haired. De-hairing is a mechanical process that separates the coarse hairs from the fine hair. After de-hairing, the resulting "cashmere" is ready to be dyed and converted into Textile yarn, fabrics and garments.

Basically, non ionic detergents are used; they are characterized by their un-charged hydrophilic head groups. It removes the dirt by the formation of micelle.