There does not appear to be a scientific term to describe a fear of The Beatles. Since your fear is to such a specific musical group, perhaps you have an aversion to a particular style of music, or to one or more members of the group.
The term to describe a fear of music is Melophobia.
If your fear begins to affect the quality of your life, or interfere with your happiness, please consult with a doctor to help you to address your fear.
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