I am certainly not that well read in religious literature but I can still put forward a conjecture. What is meant by reducing our general conceptions to unity ? By reducing our concepts to unity, peirce may mean explaining diverse things using one idea. So we explain the multitude of the qualities, relations and representations of dogs, cats, humans, apes, elephants, giraffes etc. by bringing them all under one concept- the concept of a mammal. How in the world is the idea of a god required for this? For that we must try to define god. God is the ultimate ideal of all degrees of truth, goodness and admirable-ness in the universe. That is why we worship god. Ideals are required for all types of unification of ideas. For that we must show that ideals are required for all the three peircean categories of thought. Thirdness or thought requires a basic reference to truth. Secondness or action requires a basic reference to the good and feeling requires reference to admirableness. In other words, if thought, action and feeling are to be able to fulfil their functions they must conform to ideals. Finally goodness, truth and admirableness in an infinite degree all united in one god/deity help to guide all the things we are capable of doing that is thinking, acting and feeling. I really have no clue about the non-controversial nature of this doctrine so I cannot answer your third and fourth questions. P.S. this is not decisive content. I can only hope that it helps to churn thought in you and others with the result that better ideas are put forward.
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