It is a small irony that the cresent moon and star were the symbols of Contantinopole. Richard I (Lionheart) wore them on his crusade as an ally of the Roman empire.
The Cresent moon references Diana/Artemis, whose priest warned the people of an earthquake, and due to his clamor, they who went to see him were safely out of doors.
The star refers to the Virgin Mary.
When Contantinopole was conquered, the Ottoman sultan took the symbol over.
“The church must strip itself of vanity, arrogance, and price.” Pope Francis