What I don't get is why are you singling out Khazar jews. You have no problem in considering Jews, who immigrated from Arabic countries, as "real" or semitic jews. But you seem hostile to Jews who immigrated from Europe (Khazar or otherwise). Why is that? Does Israel' say anywhere that it only belongs to semitic jews?
Judaism is a religion, not a race. A khazar can be a better "jew" than a Moroccan jew, based on how well he/she adheres to the principles of Judaism.
While Khazars didn't defeat Arabs, the fight was pretty much a stalemate. However, what is clear is that Khazars stopped Umayyad Arab empire from conquering Byzantine empire or Europe completely.
Because it has been proved that the Ashkenazi Jews are the biggest troublemakers. They brought Zionism etc. They were the ones who were hated by everyone who surrounded them in Europe while the Mizrahi and Sephardic Jews were well-liked and lived in peace with their neighbors.
The Ashkenazi Jews were founders of such bloody ideologies like communism etc. Many of them were leading elements in the USSR and we all know about their crimes.
Later the same people came to Palestine and caused problems again. I also stated that Zionism is shared by not only Ashkenazi's just as not every Ashkenazi is a Zionist.
I already said that this is the case. Same with Muslims and Christians. Nobody said anything else. We were talking about genetics, history etc.
Since you are a Jewish convert (I presume) then you most know that there are certain families in Judaism that have certain responsibilities. Such as the Cohen etc. All those families take pride/must trace their ancestry to the earliest Semitic Jews.
Well as I told you the early Arab Caliphates conquered and defeated Europeans, Romans, Byzantines, Turkic peoples, Han Chinese, Caucasians, Jews etc. In fact everyone they met on their way.
They already controlled the vastest empire of that time and more conquest would not have been possible on the long run. There are limits to everything. Moreover I doubt that they had any interest in Northern/Central Europe which at that time was completely useless and without any major civilization. Aside from Vikings and pagan Germanic tribes.
The Eastern Byzantine empire fell and the richest areas came under Arab/Muslim control at that time.
Anyway this is not important.
Regarding the Jews on the Arabian Peninsula. Many also converted to Islam and merged with the Muslim population. Some migrated outside of the Peninsula completely. Some to Yemen. Others elsewhere.
But those Jews had nothing to do with the Ashkenazi Jews of today though.
Some were not Israelis/Jews but just Arab Jewish converts.