They often ask if Islam is compatible with the West or if it's even possible to think of a "real" Westerner who is also a Muslim. They forget that in some countries and areas of Eastern Europe, Islam is the religion of the indigenuous.
To be a Westerner and a Muslim at the same time is of course possible. Although as a Western Muslim, of course you'd likely be more influenced by the Middle Eastern culture. Just like Western Europe is much influenced by the Roman culture that it looks up to.