Wilde's older sister, Chloe Cockburn, is a civil rights attorney in New York; her aunt, Sarah Caudwell, was a writer; her half-cousin, Stephanie Flanders, is a journalist; and her paternal grandfather, Claud Cockburn, was a novelist and journalist.
Njen oče, Andrew Cockburn, ki se je rodil v Londonu, Anglija in odraščal na Irskem, je novinar, tako kot njena strica Alexander Cockburn in Patrick Cockburn (vsi trije pišejo za politično spletno stran CounterPunch.org).