Just to clarify, I'm asking you to assign an alignment to the idea of creepy spiders in the abstract. I personally lean towards neutral because I don't find spiders scary until they are touching me, and I can't find jumping spiders scary at all. But I want to find out what other people think.
Fear of spiders is an inate defense response passed down by survivors of spider encounters. It is a behavior accessible to creatures of all alignments.
How funny would it be to have the BBEG & an arachniphobic paladin cluch eachother in fear of a wildshaped giant wolf-spider?
Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering.
Since darkness is traditionally liked to evil the "Dark side" is so aligned to. And Fear is thus the path to Evil leading to the conclusion that Fear, and being filled by Fear, is aligning, or being aligned to, Evil. So on the Good-Evil axis Fear of Spiders is aligned to Evil. Fear being an emotion have no intrinsic aligned towards Order or Chaos, how it affects the person is individual.
Therefore Fear of Spiders (arachnophobia) is Neutral Evil.