"born in the purple"
Royal purple
Creative Commons AttributionRoyal purple - Credit: Patrick Hoesly
King George VI wearing purple robes
Public DomainKing George VI wearing purple robes - Credit: Gerald Kelly
A queen wearing a purple robe to signify her royal status
Public DomainA queen wearing a purple robe to signify her royal status - Credit: Joseph Martin Kronheim

purple crown
Creative Commons Attributionpurple crown - Credit: dbking
This expression refers to a child born to a reigning monarch, purple being a customary color for royal garments.