Catholics came on the island with the Venetian nobles who ruled the island for centuries. They were usually rich and lived inside the 5 castles of the island, contrary to the Orthodox, who were mainly poor peasants. They had to rent and cultivate the land and lived in the cave houses or in the hinterland.
The two doctrines coexist peacefully, so several churches have two different altars. It’s up to you to discover them!