Modern Israel Aren't Real Jews?

Stop and listen a second 

1) Over 50% of the Jews in Israel are Sephardic or Mizrahi Jews, i.e., Jews native to North Africa and the Middle East. 

2) There has been a consistent Jewish presence in Palestine for thousands of years, e.g., Hebron has Jews that have lived there for 3 Millenia.

3) Many Ashkenazi Jews came from Jews that that the Romans enslaved after the Bar Kokhba revolt in the 2nd Century, long before the supposed conversion of the Khazar tribe to Judaism.

4) If Ashkenazi Jews are descended from the Khazars why do none of them have Turkic surnames??

5) In fact there are Ashkenazi Cohens and Levis, who are descended from the priestly tribe and the tribe responsible for the temple. They cannot be converts. Their lineage comes via their father.

6) Multiple DNA studies of Ashkenazi Jews show the carry DNA common to the Levant.

7) The Khazar Conspiracy theory has long been debunked and is only perpetrated by ignorant Westerners and Muslim propagandists seeking to undermine the legitimacy of Israel.