The answer is maybe; the point is debatable; the issue is very complex and politicized.

While Bernard Lewis' Semites and Anti-Semites is extensively quoted on the subject, I would caution that a) it's a survey-level text and b) Bernard Lewis is criticized in some circles as a biased source. Edward Said himself was critical of Bernard Lewis, as he explained in Orientalism, claiming Lewis' translation of an Arabic tract "[hinted] much more broadly than is usual for him that the Arab is scarcely more than a neurotic sexual being." In fact, Said accused Lewis of being a classic western Orientalist. I am not suggesting anything similar, only further explaining that when I say it's debatable, I mean it.

Some others, including myself, favor another interpretation, which is that the more virulent form of modern anti-Semitism in the Arab World originates from Colonialist policies in which Imperial Powers - namely Turkey, France, and Britain - fostered policies that favored whites and non-Arabs in Colonial-Arab territories. In many cases they extended these policies to native Arab Jews and Christians; in other cases, Jews and Christians felt more welcome, or took further advantage of the opportunities, to assimilate with the Imperial power. Regardless, there was a certain level of socioeconomic mobility in Arab Jewish and Christian groups in colonial society. This led to resentment from neighboring Arab groups that exacerbated lingering historical antisemitism and anti-Christian sentiment in the Arab world. However, this did not necessarily lead to direct conflict: Arab Jews and Christians participated in Arab anti-colonial movements.

So how from active participants in Arab daily life to the hated enemy? Ultimately, all roads of modern Arab anti-semitism lead to the founding of the State of Israel. At first, a majority of Arabs believed the creation of Israel was ordered and armed by the very same (hated) colonial powers who had ruled them for hundreds of years. That initial perception of Israel as a colonial bulwark or even colonial power in its own right has evolved over time to something more sinister, and is outside the scope of your question but is worthy of further reading.

However, what makes the Jewish narrative compelling evidence for the Colonial theory, is how similar it is to the Christian one. Arab Christians are also seen as agents of colonialism. After WW2, many Arab nations attacked their Christian populations or enforced discriminatory policies on them, leading to emigration or, in the case of Lebanon, rebellion. This has only accelerated today as another "Imperial power", the United States, has entered Middle Eastern politics. The narratives one reads today about Christians in the Arab World could be lifted from 1948 Iraq, almost word for word.

Tl;dr it's all Europe's fault. Maybe.