If anything, the Muslims inspired the Nazis as well as the other way round. Many of the tools of dhimmitude were recycled by the Nazis. The requirement of being marked in public, for example. This is why so many Nazis were able to fit into the Arab societies after they fled Europe.
Numerous Nazis found shelter in the Middle East, especially Egypt and Syria, after the war, as well as employment in their security services and propaganda ministries. Some even converted to Islam, finding in it the fullest expression of their fascism. In this sense Nazism played a direct role in shaping the modern Middle East.
Three elements drew Arab and Muslim leaders to the Nazis. First was Muslim theological antisemitism, which meshed well with Nazi racist antisemitism. Muslims needed no lessons regarding Jew hatred. The Koran and other Islamic sources are filled with verses reviling Jews as filthy schemers and betrayers of the prophet and calling for their mistreatment and murder. The lengthy history of pogroms against Jews in the Arab and Muslim worlds shows these theological exhortations were taken seriously. New, however, was the language of Jews as vermin and the fantasy of a single global Jewish conspiracy. Treatment of Jews in Germany also emboldened Muslim anti-Semites who were encouraged to prepare their own attacks.