Question

which cultural element was common to all Greek city-states?

Answer 1

All the ancient Greek city-states had a common culture, religion and language. Outsiders who did not speak Greek were considered to be barbarians.
The ancient Greeks shared a common heritage. Despite this, each of the city-states or "poleis" was an independent political unit with its own laws, customs, money and military force.
The geography of Greece played a key role in the development of city-states. The country was surrounded by the Mediterranean and Aegean Seas which provided the Greeks with easy access to water. Its mountainous regions led to the formation of unique and independent city-states. The most prominent Greek city-states were Athens and Sparta.