Final answer:
Cortés leveraged both diplomatic and military tactics in response to religious differences, initially positioning himself as a purveyor of Christian doctrines to the willing Aztecs, then using force and alliances with dissatisfied native groups to raze Tenochtitlan, replacing indigenous practices with Christian ones.
Step-by-step explanation:
Hernán Cortés' approach to the religious differences he encountered in the Aztec Empire was complex and strategic. Upon his arrival and subsequent interactions with Emperor Moctezuma II and the Aztec people, Cortés exploited Moctezuma's belief that the King of Spain might be their natural lord and that the Spanish represented a power that should be appeased. Cortés also took advantage of the Mexica's initial welcoming attitude and eagerness to learn about Christianity, as he later remarked on their willingness to accept new religious ideologies. He reported a passive acceptance among the natives when he 'purified' their temples, removing their idols and introducing Christian symbols instead, and even their adaptation to his ban on human sacrifices.
Despite these ostensibly peaceful religious reforms, Cortés's actions ultimately led to the destruction of the Aztec Empire, a process facilitated not only by his military conquests but also by an environment ripe with native conflicts and the introduction of European diseases like smallpox. The friars that followed, such as Dominican friar Bartolome de las Casas, attempted to build upon this religious conversion, advocating for the dignity and humanity of the native populations and their conversion to Christianity, bridging the gap between the two societies.