Unfortunately, being part of the same culture does not preclude people from having conflicts with each other. The desire for self-preservation and one's own comfort takes priority over shared cultural traditions and values.
If you look at history, however, it is evident that most of the big conflicts take place between different cultural groups—right wing versus left wing; Christians versus Jews; natives versus colonists and the like.
The existence of human emotions like greed, jealousy and anger mean that conflict will always be part of life. The conflicts that happen within cultural groups are likely to on a smaller scale than conflicts that take place between cultural groups. They will be around petty issues as opposed to the deep ideological rifts that create intercultural conflicts.
Yes, conflict is inevitable in every society, and much of social science is concerned with what to about this. How does a social group or culture best channel the inevitable aggressions that arise...
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