BA is a game built on vibes, and tells you not to think hard. There is lore but it doesn't matter compared to the story of youthful vibes.
Like we know that alt races in this world exists, it says Aru is a demon on her driver's license, logically the other people in the world would also know horned people are demons. So why would the occult club be trying to summon a demon? The answer is don't think. It's vibes. Unless Wildhunt is extremely out of tune with the rest of the world somehow.