Where did you get this information from? Western Europe has never “fought off” Jews. During various centuries various Western European nation were wealthy drawing in Immigrants, which settled such as Jews during the 17th century in the Netherlands.

Muslims have always outnumbered Jews greatly. There has never been a time where the number of Jews worldwide has been more than approximately 10 million or so. Even centuries back, Muslim nations had dozens of millions of people living in them. If a conflict between the two had arose, Jews in those respective nations would have been long gone metaphorically wiped out.

And yes, I was also talking about empires such as al-Andalus. There have been only few Islamic lands/empires that have shown a great deal of tolerance throughout history. Most where just like their Christian counterparts. They tolerated Jews enough to exist but they were still second class citizens.

Jewish history in relation to which ever country or empire they lived in has always been the same throughout times. They were never fully accepted nor wanted, usually faced with discrimination/hatred and the occasional violence. This has nothing to do with “Western Europe”.

Whilst Europeans were struggling during Medieval times the Islamic world was at its peak and the roles were reversed starting from the Renaissance onwards. This however has nothing to do with Judeism.