If 'the West' is primarily made up of people who think like you then good riddance. OTOH, the rest of us are adaptable and curious. We like new cultural synthesis; new immigrants are a source of fun new restaurants, new media/arts, and new ideas to explore.
People have been sounding the call of '[People who look different] are coming! Our culture is doomed!' for mellennia, and thankfully we learn not to cares what they think. We will keep progressing and leave them to stew in their ignorance and spite. For more than 2000 years people complained about the barbarians invading, but once we learn to ignore the shrill cries of alarm we look around and the barbarians are nowhere to be seen, just a bunch of new citizens with interesting new ideas.