Pogonophobia
Pogonophobia is the fear of beards.
The term pogonophobia is derived from the Greek words pogon (πώγων) for beard and phobos (φόβος) for fear. Its antonym would be "pogonophilia", that is the love of beards or bearded persons.
David Smith's 1851 publication of The Covenanter of the Reformed Presbyterian Church describes the Jesuits of Baden as suffering "a veritable pogonophobia at the sight of a democratic chin."