Secondly, the Crescent moon is not an islamic symbol but a Turkic one -- used by Turkic empires including Buddhist and Nestorian Christians and Manichaen
The swastika symbolizes the Hindu wheel of life. In Vietnam I saw swastikas worn by Buddhists. American Indians revered the swastika symbol.
But both the swastika and the crescent moon got permanently hijacked by dark forces & will always be associated with them. Mosque domes topped by the crescent & star have nothing to do with the Ottomans.
The Vatican website doesn’t incorporate the crescent by a long shot. For one thing, the horns of the Islamic crescent are normally pointed to the right.