It seems like you’re speaking of naturalism as defined in lay terms. But the presumption of lay naturalism is generally consistent with the view of metaphysical naturalism, which says that all of reality is reducible to natural explanation.
For this reason, the most honest among metaphysical naturalists admit that thought, intentionality and self are not explainable by natural causes and therefore they are not part of reality. They don’t exist.
“intentionality and self are not explainable by natural causes “
Really? That’s a bold assertion. They are clearly observable. They have been studied for a very long time with much commentary.
Seriously, you need to recognize that statement -- stripped of it's qualifiers -- as not just a lie, but a d*mned lie.
You must comprehend that the scientific enterprise is not, and certainly was not, based on your "metaphysical naturalism", which denies all reality outside the natural realm, but rather on methodological naturalism, which simply sets aside all super-natural processes and explanations, for the purpose of scientific investigations.
That the "public mind" is totally confused on this subject is certainly the result of very aggressive atheists blurring the distinctions, and true Believers cowering in the face of "politically correct" onslaughts.
Indeed, it seems to me that some "fundamentalists" encourage the confusion, as a way of more sharply dividing their own faith from, let us call it: "worldly science".