The civilization that left local customs alone when a city was conquered was the Aztec Empire.
After the Aztecs conquered a city or a people, they would allow those people to still keep their local customs and cultures. They would however requires that the conquered people accept the Aztec god Huitzilopochtli into their own system of beliefs.
This made it easier for the Aztecs to control their empire as people would be less likely to rebel since they were able to keep some of their culture.
This does not mean that the Aztecs were benevolent leaders however as they would sometimes demand a human tribute from the cities they conquered show would then be sacrificed to their gods.
In conclusion, the civilization that would often leave local customs alone when a city was conquered were the Aztecs.
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