I am a Philosophical Naturalist. Given what I have seen of the world:
There is no reason to assume the existence of anything supernatural. While there may continue to be unexplained phenomena for as long as the human race exists, every phenomena we ever have found an evidence-based explanation for has turned out to be natural. If it turns out that psychic powers exist (still waiting for that evidence), they will turn out to be a natural phenomena. In fact, the universe is defined* to be everything that exists. If there are fairies or leprechauns, they have to exist in the universe. They will turn out to be just as natural as the celestial realm of the stars.
This is a slightly different position than many scientists take. For scientists, the position is Methodological Naturalism. It's more like this:
All we can detect is the natural world. If something is supernatural, we cannot know anything about it. It is not measurable, and therefore cannot be used as an explanation for things that are.
It's a great start. It's what let great thinkers like Newton become scientists. You can be religious and still be a scientist. You just have to check your supernatural explanations at the door. Supernatural explanations can't explain real phenomena. Which is why Newton came up with a natural explanation for the falling apple, rather than saying "Angels make the apple move".
But Methodological Naturalism falls short. If only the natural world is detectable, why believe in the supernatural at all? Something that exists, but doesn't in any way affect the natural world is indistinguishable from nonexistant.
*Universe: "the aggregate of all existing matter, energy, and space" - if we find something that isn't matter, energy, or space, we'll have to update the definition to include it.