The question isn’t whether there’s a “higher intelligence”, but whether such an intelligence is supernatural. The religious argue that their god or gods are somehow outside of nature without ever addressing the how and why of such a concept.
And there are the claims that god is invisible, intangible, omnipresent. Something that’s you can’t see or touch and is everywhere is functionally identical with something that is nowhere and doesn’t exist.
I also like to compare the Christian god with Superman. Superman started out with basic superhuman powers, such as jumping over buildings and lifting heavy things. Then he acquired invulnerability, superspeed, x-ray eyes, etc. This power bloat destroyed the drama because nothing could touch him. So they had to invent kryptonite. Similarly, Jehovah went from a powerful tribal warrior god to the ultimate omnipotent boring superhero, so they had to invent Jesus, who could be tortured and killed, to bring a little drama into the fable. Spoiler: Jesus comes back to life on the last page of the comic book.
I care about all this bullshit to the extent that it causes harm in the real world.