Well one problem with "atheism" as "a lack of belief ..." is when some start extending this to babies, so babies become atheists. Under that extension of the meaning cactus are atheists.

Yes the use of the old fashioned "naturalist" is also problem. However, I think the main problem is almost the opposite of what you describe.

The generally relevant meaning of "naturalist" in discussions around atheism/gods (and morality and science) is as a differentiator to the rationalist. When contrasting these two positions the "naturalist", in differentiating themselves from the rationalist, means to allow for the conceptual possibility of the supernatural. That is, that even if there where supernaturally existing entities their character, and the possibility of knowing these, is not to be found by pure reason. So there is a sense in which "naturalism" is a problem because it excludes the "supernatural".