Historically speaking, the British Israelite movement has sought and seeks to prove that Europeans of Northern and Western descent, especially the royal family, are directly related to the Ten Lost Tribes of Israelites from the Old Testament. Most of these ideas were taken metaphorically from Bible passages, or from flawed/misunderstood archaeological digs in the Middle East, and have certainly been proven false by modern-day genetic testing and archaeological advances.
These British Israeli groups were once as widespread as the British Empire itself, with offshoots appearing in New Zealand, Australia, Canada, and the U.S., though there never existed a unified, organized body of British Israelites. In the United States, the largest of the British-Israeli organizations was the Anglo-Saxon Federation, founded in 1933, though this organization remained small and existed more on paper than in any real sense of a larger movement.
It was after the British Israelite movement had breached American shores and taken a moment to breathe that it began to change and evolve. The American British Israeli movement became infected with the latent anti-Semitism present in the U.S., in direct opposition to the Jewish-supported and Jewish-supporting British Israelism in the United Kingdom. American BI no longer believed that contemporary Jews were the children of Judah, but instead that they were Khazars (basically false Jews) and were to be hated.
Besides the core belief Germanic, Nordic, and Anglo-Saxon superiority through direct relation to Abraham, Isaac, and Jacob. Christian Identists believe that Europeans are the "Chosen People" and all others are descendants of Cain. To Christian Identists, all non-Whites are to be enslaved or exterminated, are soul-less, and cannot achieve salvation. It is anti-Semitic, Creationist, espouses Holocaust Denial as well as Millennial thinking believing the world will end in Race War or Jewish-backed UN world takeover. Books like Protocols of the Elders of Zion, The Myth of the Six Million, and Communism a Jewish Talmudic Concept and more of the like, tend to show up on their reading lists.
Important early figures in this transformation from British Israelism to Christian Identity are Reverend Wesley Swift, who started his own “Church of Jesus Christ Christian” in the 1940s. Rev. Swift quickly became associated with Gerald L.K. Smith, one of the most prominent early Fascists and ideologues in the U.S. His association with Smith, whose numerous allies stretched from the Second Ku Klux Klan to the German-American Bund and many other early far-right key figures and organizations. Through these connections, Christian Identity found itself further wedded into the American far right and further radicalized its racist and anti-Semitic stances.
Swift exhibited further influence in the ideologies of his students, James K. Warner, William Potter Gale, and Richard Butler. All three became major leaders of the far right and more radical "Hate Right," even into the present day. Warner worked to defend segregation in the fifties and sixties; Potter Gale later went on to found the Posse Comitatus movement (progenitors to the modern militia movement, sovereign citizen movement, and the movement to which the Waco bombing can be attributed to some degree); and Butler probably rose to his highest prominence after creating the Aryan Nations, whose constituents would go on to commit a number of hate crimes across the United States.
Resources
Religion and the Racist Right: The Origins of the Christian Identity Movement by Barkun
God and Race: British-Israelism and Christian Identity by Ingram
Ingram and Barkun are two good introductory texts on the Christian Identity Sect, though there is still plenty of work to be done regarding certain smaller aspects and influences on the "Church"
