Douglas Harper's Etymology Dictionary
chaetophobia
"fear of hair," from chaeto- "hair; bristle" + -phobia "fear."
Wikipedia
Chaetophobia
Chaetophobia is fear of hair, a type of specific phobia. Sufferers' fear may be associated with human hair and/or animal hair. They fear people or animals with an excess amount of hair. They may also fear the hair on their own body. Some only fear detached or loose hair and do not mind attached hair. The term chaetophobia comes from the Greek χαίτη - khaitē, meaning "loose, flowing hair" and φόβος - phobos, meaning "fear".)