Pogonophobia ... pogon for beards and phobia for fear.
Stache-a-phobia
The irrational fear is called a phobia; the experience or object that triggers a phobia could be called a phobic experience or object.
the only phobia of the fear of crickets is crickephobia
Bebuphobia...that is the fear or phobia of blueberries.
To have a phobia is to have a fear.
I know of no phobia named for the fear of mustaches. Chaetophobia, Trichopathophobia, Trichophobia, and Hypertrichophobia are names of phobias relating to the fear of hair. It could be that people believe than a person is hiding something behind the mustache. Some people believe that a mustache makes a person appear shady, for some reason. Some perverts that have had their faces on the television have mustaches, there may be something connected to that. Disclaimer I may be very wrong in my assumptions or have missed something, and everything said is subject to change, new discovery,extinction, or Webster's dictionary adopts a new word.
Mud Phobia is the phobia (fear) of mud. Its called mysophobia, myso meaning mud and phobia meaning fear.
Atychiphobia (kakorrhaphiophobia, fear of failure, fear of failing, failure phobia).
Theophobia- the irrational fear of a god or deity. Remember its only a phobia if its an "irrational" fear, a normal healthy fear is not a phobia.
There is no medical term or phobia name for the fear of immigrants.However a similar phobia called Xenophobia is the fear of foreigners.
We use the term phobophobia to name the fear of fear or of phobias. (The word phobia comes from the Greek for fear.)