The Muslim immigrant does not trade one national identity for another. What he does is bring along his local ethnic identity and his global religious identity, and unpacks them both in Sydney or London where he is a member of an ethnic community and a religious community. On top of that he may be an Australian, but he is an Australian in the same way that Sunnis and Shiites are Iraqis or Syrians. All that means is that he will pay taxes, fill out forms and curse the local government officials for being incompetent blockheads, instead of the ones back home. And when his religious identity is at odds with his national obligations, he will do exactly what Sunnis in Syria or Shiites in Iraq have done. He will choose religious identity over national identity.
