There are many people who do not become "culturally adapted" to their environments, especially nowadays when people have free access to the internet. I've seen ex-Muslims who are stronger defenders of Western values than the Western people themselves, partially because they know about the alternatives.
Those kinds of people should always retain the right to immigrate to Europe. The people who obviously do not give a damn about European values, and instead want European to conform to their values, ought to have stayed where they belonged.
Like I've said previously in this thread, some people are born more adventurous than others, causing them to abandon their cultural values in favour of better ones, or atleast new ones. Most will stick to they what they have been taught, and those people are obviously better off staying in their own countries, to avoid the trouble.
Sure. Diversity can be avoided through proper integration of the immigrants. At that point, the only thing separating the two people is their skin color, not their language, religion or ideological values, and that is ultimately not enough to cause a conflict. You need a variety of divisive attributes to cause a conflict to take place. The perfect storm is a situation like the secular Western man and the religious Arab Muslim.