All cultures change, and just because immigrants immigrate to other countries doesn't mean that culture is going to be erased. Future generations will decide what kind of culture they want to live in, and what constitutes national identity. It's not going to be decided by the generations on their way out.
Even in Japan, which is a very nationalistic, and tightly controlled culture, is experiencing a shift in their culture due to globalization. They are being influenced, and some old ways are dying. It's normal. The future isn't there to please past generation's. The globalization of pop culture alone has greater influence on cultures than immigration does.
Much of radical Islam's resentment has to do with what they see as the ever increasing liberalization of their culture, and their religion. It's a nationalistic resentment, as much as it is a religious one. In many Islmaic countries, they're entwined. Both nationalism, and religion tend to attract the same personality types. Both have been horrible mechanisms for keeping people safe, and are good at causing deeper problems for their countries.
Homogenized cultures are no longer useful. It's a feature of the past. Most traditions are pointless, and can be shed without much consequence. Traditions that last tend to do so because they serve a purpose. The ones that stop serving a purpose, face backlash, erosion, and ultimately, abandonment.
Globalization is natural. Tribalism is not. Tribalism made more sense when the world was smaller, and allies and resources were not as accessible as they are now. Trade has reduced its practicality even more.
Nationalism divides people, and makes them more likely to attack others, and more vulnerable to being attacked themselves. Again, it's very similar to religion in its negative influence on how people think. It can make them less ethical, and less sympathetic toward other human beings.
