Atheistic Supernaturalism

The concept of atheism, that no gods exist, and the word atheism itself are culturally assumed to be related to a philosophy which totally excludes belief in supernatural things or the very possibility of them.  In reality, the concept of naturalism, which is the idea that nothing nonphysical exists or that all immaterial things metaphysically spring from matter, would entail atheism, but atheism does not entail naturalism.  When focusing on this comparison without making assumptions, it is very easy to understand this, but everything from superficial presentations of atheists in entertainment to casual conversations with the typical non-rationalist reveals that it is fairly common for the two ideologies to be mistaken as synonymous.

Not all existing or logically possible things of a supernatural nature--which only means they are not physical, not that they are bizarre--are deities, so specifically believing that there is no god of any kind, as idiotic as that already is due to the logical necessity of an uncaused cause and the epistemological impossibility of disproving an uncaused cause's existence even if it did not exist, would not require belief that all other nonphysical/supernatural entities or metaphysical existents are not part of reality.  This would be naturalism, not atheism.  The two often get conflated by theists and atheists and by supernaturalists and naturalists alike.  So conflated are these two ideas that to even mention that someone could be a sincere atheist while actively rejecting naturalism, because atheism would not logically necessitate the nonexistence of anything immaterial, would probably be misunderstood by most people immediately.

It is possible to understand the fundamental concept of atheism (the nonexistence of all deities) and of naturalism (in its strictest form, the nonexistence of anything immaterial) without realizing this distinction, yes.  This is just not all that can be known about the conceptual relationship.  It would be unusual to actually find a self-professed atheist who says he or she believes in other supernatural things besides God (things like consciousness are nonphysical and not part of nature, thus making them supernatural in a looser sense of the word, but this is not what most people seem to mean by the term supernatural because they are focusing on spirits without bodies), but this is in truth more because of the common misconception that atheism is naturalism instead of just one component of naturalism, which atheism does not encompass the whole of.

An atheist could believe in witchcraft, that ghosts of dead humans exist after the death of the body, or in an afterlife in a realm that transcends nature, all without actually contradicting their atheism.  The problem is not the fact that atheistic supernaturalism defies standard misconceptions of what atheism and supernaturalism really are.  Atheistic supernaturalism is philosophically false not because there is anything incompatible about atheism and supernaturalism, but because atheism is false due to the existence of the uncaused cause, one of the only things that can actually be proven to exist [1].  It is actually the external world of matter that is extremely difficult to prove the existence of, and even then, if atheism was true, things like the laws of logic, metaphysical space matter resides in, consciousness of any kind, and time would still be nonphysical existents and require that naturalism is false.

[1].  https://thechristianrationalist.blogspot.com/2017/04/the-uncaused-cause.html