We should not make excuses for people who are uncomfortable with difference. The sentiment that different cultures represent a direct threat to your own culture is an irrational racial prejudice, and a form of xenophobia.
Although the values of other cultures may test our own, this is not necessarily a bad thing. If a set of beliefs or values are right, they should be able to withstand criticism and open debate.
Anti-immigration proponents typically focus on the worst cases of culture clash, which only apply to a tiny minority of migrants. The number of people with extremist views in the native population of any given country is bound to outweigh the number of extremist migrants.
Different ethnic groups enrich culture rather than destroy it. Culture is not static; it's constantly evolving through new forms of stimulus. Some people believe in the perpetuity of culture, but this argument is based on fear and lacks both proof and substance. Many people enjoy the benefits of a multicultural society, from foreign foods to new ideas and music.
Research shows that while integration takes time, it does eventually happen. The children of immigrants are normally completely acclimated to the new culture.