Hypertrichophobia
This is a specific anxiety disorder that describes the pathologically exaggerated fear of (too much) hair. The sufferer avoids hair mainly when there is too much hair, and thus hairdressers, hairdressing salons, people with long and/or a lot of hair, etc. a. from body hair, from animal hair or from your own hair.
The word comes from the ancient Greek: hyper = over or too much, tricho = hair and phobia = fear.