In September 2015, Spector married actress
Rebecca Hall, whom he had first met the year before, during their work together in the Broadway play
Machinal. Spector is a member of the
Democratic Socialists of America and helped produce the documentary,
The Big Scary "S" Word. In 2024, along with 30 other artists, Spector participated in publicly reading the dossier of
South Africa's genocide case against Israel, which was brought before the
International Court of Justice. The reading was organised by Palifest. In September 2025, Spector signed an open pledge with
Film Workers for Palestine promising not to work with Israeli film institutions "that are implicated in genocide and apartheid against the Palestinian people." ==Filmography==