Does he believe in the supernatural? Is he superstitious?
Not completely. Iwaizumi thinks he’s had his fair share of ghost experiences (though most of them were when he was younger and had an imagination that would never rest), but he can’t recall them in great detail, and he knows that he was never scared of ghosts. He does, however, know for a fact that “monsters” aren’t real; he watches so many monster movies that he’s adjusted to the idea of them and they no longer scare or threaten him. They’re purely fictional in his mind.
He’s not very superstitious either, and sometimes goes to the trouble of messing up superstitions out of spite (i.e. someone may think its lucky to twist their pencil at a certain degree on their desk, and Iwaizumi will turn it straight when they don’t notice). That’s only with people he knows well, though, because his friends all know about his dislike for superstitions and would understand his actions. And most of his distaste for it comes from the idea that people are obsessed with “forces they can’t change,” which means that--- if a pre-determined fate or destiny was real--- there’s no way to stop these things from happening, even if they can supposedly be “warded off.” But in fact, Iwaizumi doesn’t actually believe in pre-determined fates or destinies, either, because he doesn’t think that a “force” who can decide them all on its own actually exists.
He’s not very spiritual in general; he bases his beliefs off of fact and rationality. I think that this may be an attribute he’s inherited from his family*, being that they worship Shintō, but not necessarily any gods or goddesses. Their faith is rooted in the moral beliefs of the religion, and often traditional practices, though they’re not meant to appeal to higher beings.
*I’m not sure if I expanded on this in the about page but I likely will in another headcanon post sometime in the near future.