McKearney lost three of his brothers during the Northern Ireland Troubles. Sean was killed by his own bomb in 1974, Pádraig was killed by the Special Air Service (SAS) in the Loughgall Ambush on 8 May 1987, and Kevin, a non-paramilitary, was murdered by the Ulster Volunteer Force (UVF) in 1992 while working in the family's butcher shop. His sister, Margaret, was the subject of an unsuccessful extradition attempt in 1975, when Scotland Yard described her as "possibly the most dangerous woman terrorist in Britain."