The family, who are of Somali origin and from the Midlands, are now in foster care.
Details of the "physical and emotional" abuse were revealed during a hearing in the family division of the High Court last week in which Justice Russell ruled the youngest child should move to residential care.
Dame Esther Rantzen, Childline founder and president, called the case "horrific".
The High Court judgment says: "The children have complained that their parents expressed support for extremist violence and have expressed anti-Semitic, anti-British, homophobic and anti-white views in the home, which the children reject."
The parents, who cannot be named, deny the allegation.