That's pure unadulterated hooey. 'Ashkenaz is the old Hebrew name of Germany and 'Ashkenazim simply means "German Jews." It refers to Jews of northern, central, and eastern Europe (those with German or slavic surnames and who speak Yiddish). Furthermore, 'Ashkenazi Hebrew and the 'Ashkenazi ritual come from 'Eretz Yisra'el while those of the allegedly "purer" Sefaradim (which simply means "Spanish Jews") comes from 'Eretz Bavel (Babylon). Sefardi Hebrew is also more influenced by the Mishnah and by Aramaic than 'Ashkenazi Hebrew.
Sefaradim (and Temanim, the Yemenite Jews) have a reputation as more "authentic" because they have lived so long in the Middle East, yet they are the historical liberals of Judaism (prior to the European "enlightenment"). Moreover whatever "Khazars" or "Sabbatians" there are are more likely to be found among Levantine Sefaradim than among European 'Ashkenazim.
Unfortunately, it is among 'Ashkenazim of the past two hundred plus years that all the leftist "reform" movements have taken hold and this has distorted their image and made Sefaradim seem more conservative.
This is the truth. But most people who spout the "'Ashkenazim aren't real Jews" line simply want to believe this and cannot be persuaded otherwise. Most ironic since the Babylonian Talmud, the bete noire of so many anti-Semites, was written by the ancestors of the Sefaradim (the ancestors of the 'Ashkenazim wrote the Jerusalem Talmud!).
Some Sabbateans became Turks after the converted to Islam. Some crypto-Sabbateans became "Donme", but they have nothing to do with Khazars.
"This is the truth. But most people who spout the "'Ashkenazim aren't real Jews" line simply want to believe this and cannot be persuaded otherwise. "
Entirely try. Kevin Brooks refuted the argument before the genetic information was in, but antisemites have the gall to cite his book as a source, while ignoring its content.