I think that part of the problem is the confusion of issues: racial, ethnic, religious, historical, military,, economic, political and others. Is it a "Jewish" problem? or an "Israeli" problem? a "Muslim" problem? or an "Arab" problem? Does questioning the legitimacy of the state of Israel mean that one is anti-Semitic or just anti-Jewish? Does supporting the state of Israel mean that one is not a racist bigot anti-Jew?
If you take a religious pov, and look at the present state of Israel as the incarnation and representation of the history of the Hebrews and Israelites, then the persecution of the Jews goes back at least to ancient Egypt. (You all know the story.) Maybe that's why we were brought up to presume that Arabs and Jews were ancient natural enemies. That's not true at all, though. But, not all Arabs are Muslims; and Muslims have rarely persecuted Jews. When we talk about the persecution of Jews after the advent of Islam, we find it took place mostly in Europe. (I don't know about Asia). The burnings of synagogues did not happen in Jerusalem. They happened in York and major cities all over Europe.
They did not occur in Spain until it became a Catholic country. (So, in 1492, all the Jews and Muslims and non-Catholics were forced to leave Spain). In that sense, anti-Semitism against Arab-Muslims is less old than anti-Semitism against Jews only because Islam is younger. Right now, today, I believe that there is just as much anti-Jewish feeling as there ever was, and that's specifically talking about Europe. Even in Germany, where there is a strong attempt to eliminate racism and anti-Semitism, there is still plenty. And, there are not that many synagogues.
Why not? Well, that's one reason why the state of Israel exists. But, it's also the cause of the Palestinian problem in the ME. European Jews were persecuted in and by Europeans. Their property and lives were taken by Europeans. Why weren't these things given back? Why weren't they awarded parts of Europe? Would that have been fair? Maybe, but that's also where it gets even more complicated. Not all European powers wanted Israel to exist. Many Jews --some who had been fighting for a state long before WW2-- thought that a state, a homeland, was necessary.
I understand their point. I think the solution is problematic. However, I also understand that the first premise of discussion must be that human beings and human life come first. Deal with people on those terms, or don't expect anyone to say "I care about you."