Pogonophobic

They are part of a noble pogonophobic tradition dating back to early Christian times, when clean-shaven Romans guarded Western civilisation against shaggy savages.

[…] knows I'm pogonophobic. When I hired him he hadn't grown his beard. Nowadays I'm not important enough to fire him.

Did you hear of the pogonophobic barber, / Who suddenly decided that he wanted fame? / But on the stage he developed nomatophobia, / And couldn't bear to hear his own name.