Von Stade's surname derives from the Hanseatic port city of Stade. One of her forebears served as Stade's mayor.
Her great-grandfather was Charles Steele, lawyer, banker and partner of J. P. Morgan. Her grandfathers were Edward W. Clucas, stockbroker and yachtsman, and Francis Skiddy von Stade Sr., importer of bristles, President of the Saratoga Association and chairman of the United States Polo Association. Her great-aunt, Eleanor Steele Reese, was a concert and opera singer who gave up music for an ascetic life of ranching and rural philanthropy. Von Stade's parents were First Lieutenant Charles S. von Stade, winner of the 1941 US Open Polo Championship, and Sara Clucas von Stade, a descendant of Jonathan Trumbull, the last colonial Governor of Connecticut, who became a valued advisor of George Washington during the War of Independence.