[ChicagoHebrew]

They call themselves Jews and Karaites, just as a Chabanik calls himself both a Jew and a Chabadnik, and a Sephardi calls himself both a Jew and a Sephardi. They don't see a contradiction. The State of Israel considers them Jews, and Karaites are eligible under the law of return, but they are listed as Karaites on their ID cards. Orthodox rabbinic Jews don't obviously consider Karaites Jewish (although that requires a tortured interpretation of Jewish law, given that Karaites descend from clearly identifiable Israelite populations), but that doesn't mean Karaites don't consider themselves Jewish. You might be thinking of Samaritans, who forcefully deny that they are Jewish.

Yes, I am Jewish, and not a Karaite. Although I sympathize somewhat with Karaites on certain issues.

[Alouette]

The Noda Beyehudah (Rabbi Yehezkel Landau) wrote some tshuvot on Kar'aim, from a halachic perspective their status as Jews is complicated. For example, if a Jew married a Kara'ite woman, and they separate, is he required to give her get?

[Cinnamon Girl]

They call themselves Jews and Karaites, just as a Chabanik calls himself both a Jew and a Chabadnik, and a Sephardi calls himself both a Jew and a Sephardi. They don't see a contradiction.

This analogy is WAY off. Have you discussed your theories with any rabbis? Sephardim, Lubavitch, Misnagdim, Ashkenazim-- all believe in the 13 principles of faith, and believe in the Oral and Written Law. They are ALL Jews. The Karaites do not believe these things. They are NOT Jewish.