What myth? They even had an autonomous region in the USSR.
Still have a nice web site:
Sorry, but the conversion of the Khazars to Judaism is not a myth. At very least the aristocracy of the Khazar Khaganate converted to Judaism in the eighth or ninth century. It seems to have been a similar process to that by which the Rus converted to Orthodox Christianity: they ‘auditioned’ various versions of monotheism and settle on Judaism.
The Khazars had good relations with the Christian Roman Empire and were allied with it against the Caliphate.