It is my contention that Jews and Muslims have diametrically opposite reactions to being in the West. The Jews were a small minority among a large and hostile Christian majority. They found ways to remain as inconspicuous and innocuous as possible. They retained their own culture, including the code of laws known as Halacha (the way), but the idea that they would have expected the larger majority of Christians to be bound by it would be ludicrous. Of course, one anti-Semitic canard was that the Jews wanted to control the world, or did control the world, but that was so far from reality as not to be worth consideration. That the Jews had influence far above their numbers speaks to their innovation and industriousness not their malignity.
The Muslims by contrast saw themselves as the replacement for the Christians and on several occasions attempted with large armies to conquer and occupy Christian Europe (in 732 at Poitiers and in 1529 at Vienna). It is incumbent on Muslims as part of their beliefs to try as best they can to ensure that the state they live in is a Muslim state, controlled by Muslims and subject to Islamic sharia law. It was a severe blow to the Muslim view of themselves as the chosen of God (in replacement of the Jews and Christians) that the crusaders managed to defeat them for a while and occupy the Holy Land. Subsequently they managed to defeat and expel the Crusaders, but it is still common for Muslims to call all modern Europeans “Crusaders.”
Jews played a significant role in the development of Western secular civilization. Think of such names as Freud, Marx, Einstein; it was my contention in an essay written long ago that the Jews were in fact a catalyst for this development (see http://jackcohenart.com/Articles/catalyst.pdf). From Berlin to Hollywood, Jews have participated in every aspect of the development of modern Western civilization. As such Jews are part of the warp and weft of this civilization, you cannot imagine it without them.
By contrast, Muslims have played a negligible role in Western civilization, notwithstanding the erroneous characterization of Pres. Obama for political reasons. The Muslim world has not adopted Western values of nonviolence in political discourse, democracy (there is none in the Arab Muslim world), and tolerance for minorities. In fact, the main political thrust of the Muslim world is still that of conquest and occupation. Certainly there are large minorities of Muslims living peacefully in the West, but the westernization and modernization of the Muslim world is at a particularly low ebb, with violent insurrections of al Qaeda, Islamic State and Taliban roiling the whole Islamic world. If only 1% of the Muslims in the West (and it is probably much higher) support these extreme movements, then following Paris and Brussels, the future looks bleak.
In conclusion, Jews have played a crucial role as part of the development of Western secular civilization, while the vast majority of Muslims view the West as a hostile competitor. The election of a western-educated Muslim of Pakistani origin, Saddiq Khan, as the Labour Party candidate for London Mayor, will be a real test of whether or not he can put his role as a Londoner before that of being a Muslim. By the way, if Trump does become President, will he allow the Mayor of London to visit the US?