There are several versions of naturalism. Naturalists share in common the view that the natural world is all there is -- there is no supernatural realm of spiritual beings. However, naturalists differ in how they define 'the natural world'. Now there are at least three broad ways of characterizing "the natural world", and so there are at least three kinds of naturalists -- let's call them 'Conservatives', 'Moderates', and 'Liberals'.
Conservative naturalists are straight physicalists -- nothing exists but the physical, and the physical is characterized by all and only the properties listed in physics and chemistry textbooks.
Moderate naturalists differ from Conservative naturalists, in that they expand their conception of natural world so as to include abstracta (e.g., propositions, properties, possible worlds, etc.). Recent proponents include Tyler Burge, Jeff King, W.V.O. Quine, Roderick Chisholm, and Kit Fine.
Finally, Liberal naturalists differ from Moderates and Conservatives, in that they admit into their ontology of the natural world the abstracta of the Moderates, but they also allow for a conception of concreta according to which they have more properties and powers than the Conservatives and Moderates allow. Thus, perhaps they're straight Spinozists, or type-F monists, or panprotopsychists, etc. Liberal naturalists include Benedict Spinoza, Bertrand Russell, Galen Strawson, Donald Davidson, Thomas Nagel, David Chalmers, Daniel Stoljar, and Derk Pereboom.
In light of this sketch of the varieties of naturalism, we see that from the fact that one is a naturalist, it doesn't follow that one is averse to entities that don't belong to the ontology of Conservative naturalism. To put it differently: naturalism doesn't entail Conservative naturalism.