Why do Catholics & Orthodox Christians have common saints?
Until 1054, the Christian Church was united, so the first saints were common to all believers. However, in the 11th century, there was a split between the Eastern and Western Churches. The Primates of Rome and Byzantium, Pope Leo IX and Patriarch Michael Kerullarius of Constantinople, discussed much in correspondence about the primacy of their thrones. Leo IX was convinced that the Roman throne was of paramount importance and the Church of Constantinople should honor the Roman Church. Michael Kerullarius, however, disagreed with him.
In 1054, because of disagreements, negotiations between the two sides reached a dead end: It came to the point that papal legate Cardinal Humbert, during the service in the Hagia Sophia Cathedral of Constantinople (today Istanbul), announced the excommunication of the patriarch and his supporters. And, a few days later, Michael Kerullarius denounced the Roman throne.
But, Catholics and Orthodox still have common saints. For example, Apostle Peter - the first Pope of Rome, St. Nicholas of Myra, St. Basil the Great, St. Ambrose of Mediola, St. Anthony and St. Pachomius the Great, Blessed Augustine and others.