It is not very believable as a phobia, but it would be the "fear of reading, writing and/or saying palindromes". It might appear as a neurotic component because of some obsession with symmetries, but it's very rare. So much so, that it does not even appear in lists of pathologies, although this may be due to the convoluted pronunciation so other simpler names were invented such as aliphobia or the not very serious aibophobia.
