While the show's premise is actually exploring just that (the notion of: if there are any supernatural forces at play?), the Kings have specifically stated that there will be some things that will be left very open to interpretation and won't be necessarily explained by "science" or modern psychology.
"One of the things we thought we could get away with more, as you get brought into the bath of the show, is that metaphors are real and realities are metaphors and you’re never sure. That little demon child Kristen saw being born in the cornfield: Was that a real experience or was that hallucinogenic and represented some emotional state? Many of the scares in the show, whether George coming at her at night or the psychological scares, I think we’re allowed to get away with them and still suggest that reality is very pragmatic and empirical." -Robert King
There are quite a few things already, within any given situation, *might be explained by science, mental illness or impairment, but not everything...
One such episode that introduces a lot of new elements is "S is for Silence". By the end of the episode, the audience isn't sure if there is a demon in the box, if the demon in the box is let loose or not, and if the bot fly can really account for the positioning of all of Fenna's Stigmatas and/or the preservation of the other monk's body, let alone a theme of "whispering" insects that have been happening throughout a few episodes...
But in later episodes post S is For Silence, viewers see this clear goo that goes through Kristen's floor that may or may not be a hallucination. However, the audience is the only one noticing it and no one else ever mentions wholes in the floor, etc. And then there is also the black/dark red goo that spouts from Fenna's mouth also comes out of Leland's mouth during an exorcism, suggesting that demons or people who are "possessed", "infected", etc may have this goo inside them playing on an alleged Demon "mythology" in-universe.
Another thing that happened was that Kristen had stopped seeing George in her Night Terrors. Dr. Boggs ends up seeing him in a hallway where he is tagging along on a case the gang is working on, eager to write a book about what they are doing. George marks his noise with soot after saying "bloop" and Kristen notices the soot in a scene that happens right after. So how is it that Dr. Boggs can now see George too? Is there really any kind of transference for that in real life? Or maybe he just got soot on him from the wall and the audience just hallucinated George, despite that Dr. Boggs was terrified. ;P
In a similar vein season two also introduces a Jinn who passes from a little girl to Kristen. All season Kristen is convinced she's hallucinating many things, including the Jinn, but at the end of the season the Jinn has passed to Leland...
So IMO I would say, while there are still some things that have pretty plausible practical explanations, there are some things that hover in gray where one may not be sure which way to go, and other things that feel like they are actually building towards a supernatural mythology, especially on the demonology side of the series. IMO they have crossed over the line and I think it's hard to deny the show has supernatural phenomenon, even though it may not be all of the time or that the mythology ever perfectly stacks up neatly.
