With your clarification, I understand what you are getting at with regard to atheistic theologies.  In a sense, even a consistent materialist has a theology -- but 'theology' in this case is roughly equivalent to cosmology: a general theory of the universe.  Socrates would argue that theism and atheism and cosmology and like studies are all pretty far from the immediate problems of human ignorance facing moral demands.  Philosophy in Socrates' version is simply the obligation to think.  But as we have noted in our discussions above, if this stripped-down Socratic quest (to become and remain thoughtful) evolves into a definite philosophy, such as rationalism or skepticism or empiricism, then this new creation is on a par with atheisms, theisms, and other isms … categorized as a definite kind of ism or view.  Then the taxonomic work you are proposing can begin. 

 The citation from the Stanford Encyclopedia begins to argue about what counts as a 'theism' and what an 'adequate idea of God' might look like.  Again I think it is germane to ask why anyone would want to make these distinctions.  For centuries, Buddhism was discounted as a religion, and was labeled as a mere 'philosophy,' because (at least in the Theraveda tradition), it lacks any reference to God.  This is an arbitrary and foolish construction, denying legitimacy to hundreds of millions of people (who consider themselves to be 'religious' and Buddhism surely a 'religion').  Thus in this case it looks like the attempt to categorize 'theisms' is a way of reinforcing one idea of worship and excluding others.  It flattens out the phenomena and refuses to recognize outlying examples that offend some or other party cause.

 Philosophy descending into 'philosophies' and 'isms' is unproblematic as long as the new creation (whatever it may be) then becomes a new object of scrutiny and has to answer the Socratic elenchus and cross-examination.  This activity seems to me the core concern of philosophy, though we often let our curiosity wander off into distant corners of the intellectual universe.  We just have to learn how to get back to the core concern of thinking.