Athiesm, Theology, and Philosophy
I understand the distinction between methods that you make. I agree with
Fooloso4 that people do not build temples to the Prime Mover.
The emphasis upon creeds is not the same amongst different kinds of worship. The difference of methods is not so much about beliefs being 'incontrovertible' as it involves a relationship to a divine agent (or agents). In that sense, Aristotle's god is impersonal in comparison to the Olympian pantheon as well as those groups gathered in particular testimonies of faith connected to a world shaped by our decisions.
So, Paul's faith, for instance, is not a good measure of what giving respect to Apollo or Dionysus involves. The differences of method that separates the 'personal' from the 'impersonal', is not self-explanatory toward the purpose of distinguishing the divine from the natural for all who try to do it. That would clump together what should be seen in contrast.
My impression from reading Aristotle is that the unfolding of beings according to their potential to become what they were meant to be is the clearest encounter with a maker of the world. There is encouragement to become 'more like' this agent but those encouragements happen in the context of recognizing that what makes us is tied to our agency no matter what.
Aristotle is not that far from approaching creation stories in the manner of Timaeus, where we are told constantly that the stories are 'likely' but cannot be confirmed. What Aristotle did with the Prime Mover is to introduce that factor as an X. He does not know the value but can proceed without knowing it. It has a function.
Paul was not content to disagree with the 'natural' world but presented his vision as a "foolishness to the Greeks and a scandal for the Jews," It was a diremption with the philosophical that became philosophical. A personal vision that would sweep away tradition and the 'thinking' of the time which others tried to heal.
That is a lot different from Apollo cutting a deal with the Furies over the limits of revenge.