Remove direct Divine Influence from the Realms after the events leading to the creation of the Drow. No appearances, no Avatars, ToT is gone, no divine speech, no Sisters, no Weave instabilities...
An example of the changes which could occur in major NPCs (starting with the sacred cow

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Elminster never encounters the influence of Mystra, remains a Rogue/Fighter, developing martial skills and founding the Order of the Sacred Harp as a front for his mercenary company. Strengthening the influence of Cormyr through his patron family Wyvernspur, Elminster becomes known as the Fist of Cormyr.
Elminster's patron, House Wyvernspur, becomes interested in the developments of his mysticism. When Finder is destroyed by his clone Flattery, Elminster and several members of his former leader's cabal battle the clone, leading to a schism between the Order of the Sacred Harp (which has exposed one of their founder's true motives) and Elminster. Dejected, Elminster draws forth a band of warriors and takes them to the far reaches of the Realms, where his talents become used by various organizations. He is under the service of (pick a nation, any nation) and has been enhanced over the years through his dealings with mages. A hatred of magic still exists within the elder warrior, but he uses its powers to keep himself alive and vital even though he has passed well beyond the limits of mortal life.
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Elminster is not completely removed from the world, but changes into a completely different character. The Harpers still exist, but are at a schism; perhaps Elminster bears a Harp-and-Hand motif for his mercenary company, and the Harpers themselves have become a far more weary, more neutral organization. Without direct interference of the gods you lose a lot of the issues of separation of powers, difficulties in meshing things... and you allow for the development of societies.