Currently the only mobs that spawn naturally in Mushroom Islands/Fields are mooshroom cows. IRL the Cordyceps fungus infects ants changing their behavior for its own purposes. They're essentially zombies. The Cordyceps spider would spawn on Mycelium and because it's permanently neutral, would preserve the mushroom island's lack of hostile creatures. The spider itself, I would imagine, would be textured to be a mixture of pink/white/green.