It is matter of debate. Karaites put the Old Testament before Talmud/Rabbinic law and consider themselves Jews.
Would you say that Protestants are not Christian because they put Bible above the Church tradition and commentaries?
There is no debate. Karaites don't consider themselves Jewish, nor do Jews consider Karaites Jewish. If you want to consider them Jewish, that is your business. You may also consider Madonna to be Jewish. That doesn't make it so. Karaites don't accept Oral Law. That makes them a different religion. How Christians define themselves is their business.
Karaites put the Old Testament before Talmud/Rabbinic law and consider themselves Jews. Would you say that Protestants are not Christian because they put Bible above the Church tradition and commentaries?
Good comparison, A. Pole. Talmudists and Kabbalists are to Judaism as Roman Catholics are to Christianity. Or, as as Mormons are to Christianity. Or, as the Sunni Muslims are to Islam.
Karaites, Protestants, and Shiites make the same claim in their respective religions. Aka the original teachings had become corrupted, overlain with human tradition, a departure from the original teachings of their respective religions.