Ada was eccentric but probably not insane. Belief in fairies and leprechauns was common in her day. Considering that she was raised and tortured by her mother, it's a miracle that she wasn't a total basket case, and she wasn't.

Personally I'm more inclined to believe in fairies and leprechauns than virgins who give birth or people who rise from the dead. Ridiculous superstitions still captivate billions of people, even in this supposedly rational materialistic age.