How did the KKK become anti-semitic? I've read before that older members of the KKK claim that it wasn't anti-semitic initially, but that became part of the organisation's ideology over time. How and when did this happen?

There have really been 3 distinct KKKs over time. The first one was created in the wake of the Civil War by Nathan Bedford Forrest and others, and its target was blacks. That KKK attacked, terrorized, and killed former slaves until Jim Crow laws created a more legal venue with which to oppress blacks. Then the KKK's size waned.

The second KKK was created in Georgia by William Simmons in 1915, shortly after Birth of a Nation was released and a few months after Leo Frank (a Jewish man) was lynched in Georgia by "the Knights of Mary Phagan" (made up of core members of what would become the 2nd KKK). In brief: Mary Phagan was a young white girl who was raped and murdered in Atlanta. Leo Frank was fingered for the crime despite lack of evidence, and anti-semitic comments were trotted out at the trial. Also, there was a large wave of immigrants to the US from Eastern and Southern Europe and Ireland that began a bit before the second Klan was founded, and a lot of anti-immigrant sentiment followed. Birth of a Nation is all about the founding of the original Klan after the Civil War, and how glorious and wonderful and necessary it was. It was by far the most popular and profitable film of its time and it inspired a lot of people to talk about/believe in the glory days of the Klan. This attitude tied in with then-popular eugenics ideals and the popular anti-immigrant ideas. Plus the Mary Phagan situation became a lightning rod for antisemitism in the US, and a large percentage of Atlanta's Jews were driven out of the state at this time. And hostility came to be directed against the immigrants, particularly Catholic immigrants from Italy and Ireland. This KKK became somewhat of a social club in some areas, while being a terrorist organization as well. Like, in Indiana, a large percentage of prominent white, non-Catholic men became members. The second klan also began adopting some of the elements of the Klan on display in Birth of a Nation that were artistic license by D.W. Griffith's but that the first Klan had not used. For example, the first Klan did not burn crosses. But crosses were burned in Birth of a Nation and so the second Klan did that, too. Because this all happened before there were Nazis, there was no influence by Nazis on the second Klan's anti-semitism. It was all American-grown. However, the second Klan died out a bit after World War II. Then, the third Klan was founded as a reaction to the civil rights movement. Their anti-semitism had a lot of influence from Nazis and the white supremacist movement.

I should mention, though, that Birth of a Nation has an intertitle (the text on the screen that silent movies have instead of speech) that can be misleading in this regard. It says "The former enemies of North and South are united again in common defence of their Aryan birthright." Nowadays, "Aryan" is closely associated with Nazis and white supremacy. but in 1915, Aryan referred to Europeans in general, not specifically blond-haired, blue-eyed northern Europeans only. So it was used in the film in a white supremacist way, but no specific reference to Nazis occurred.