Many people have made the argument that difficulties for materialism need not be difficulties for ontological naturalism. But that leaves an important question: what is a non-materialist naturalism supposed to look like?
I can imagine a form of naturalism in which God, angels, and what we used to call human souls are part of nature. But then we could even imagine the physical in such a way that all these things are physical. When I took a course on physicalism with Hugh Chandler, who eventually became my doctoral dissertation advisor, he suggested that the physical is whatever is quantified over in an ideally completed physics. Since some theories in physics quantify over God, on that view, God would be physical.
Such definitional liberality, however, would make it difficult to define even methodological naturalism, since it would then no longer exclude what most of typically think it is supposed to exclude.