Muslims living in non-Muslim countries
Islam absolutely allows Muslims to settle in a non-Muslim country provided the rules of Islam can be followed. Emigration is not necessary for Muslims but is allowed only when the need arises as Prophet Muhammad (Sallallahu alaihi wa sallam) told the Companions in Makkah:
لو خرجتم إلى أرض الحبشة فإن بها ملكا لا يظلم عنده أحد وهي أرض صدق، حتى يجعل الله تعالى لكم فرجا مما أنتم فيه.
Translation: It is good if you go to Abyssinia because the king of that land is such that in his land nobody is oppressed. It is the best land until Almighty Allah opens a better way for you.
In the same way the Holy Prophet Sallallahu alaihi wa sallam ordered the Companions to go to Abyssinia even though the king of that land was non-Muslim and the government was a non-Islamic one.
The travels of the Companions to non-Muslim lands and their settling down in those lands is well established. When Islam permits Muslims to live in non-Muslim lands, the question is how should our relations with them be? The Holy Quran and the Hadith have clear commandments about this. When Muslims go to any non-Muslim land and settle down there, then through the passport and the visa they make a kind of promise to follow the country's laws. To fulfil this promise is necessary. As Almighty Allah says:
وَأَوْفُواْ بِالْعَهْدِ إِنَّ الْعَهْدَ كَانَ مَسْؤُولاً
And always fulfil the promise. No doubt, the promise will be questioned about.