One of my favorite contemporary thinkers is Cardinal George Pell of Australis. I have posted from his thought several times. (search this site for Pell) Here are excerpts from his address on Muslim immigrants in Australia.

All those who choose to come to Australia come as immigrants, not as colonists i.e. they should be committed to freedom and democracy, refrain from advocating violence or indulging in hate speech, while their political allegiance must be to Australia, not overseas. All immigrants, Christians, Muslims, non-believers should meet these criteria.
. . .
Obviously I speak as a Christian and a Catholic, committed to one version of the principle of reciprocity. Not an eye for an eye and a tooth for a tooth, but commitment to the principle that the rights we justly offer to all citizens here, including Muslim minorities, should be rights that are enjoyed by non-Muslim minorities in the Muslim world. This is not the case as I believe this conference could not be held in Pakistan or Saudi Arabia! In fact Christians are being harassed and even persecuted in many countries ranging from Nigeria, through Sudan, where some are being sold as slaves, and the Middle East to Pakistan and Indonesia. I would like to know where our friends stand on these matters.
. . .
In a pluralist and free democracy every group is criticized at some time or other. As Prime Minister Howard remarked last year, if Catholics rioted every time they were criticized there would be regular riots! It is not appropriate that Muslims regularly reply to criticism with insults, denigrations and evasions, while avoiding the point at issue. We have seen too much of this from some Muslim personalities.

Within a secular democratic society harmonious integration of minorities is achievable because all citizens, belonging to the majority culture, or minorities, are acknowledged to be equal in the eyes of the law. Equal rights, however, carry with them equal responsibilities. Problems arise when minorities demand special consideration that places them outside the law as it applies to all other citizens. Flexibility and adaptability are called for when refugees and immigrants arrive in a host country. But there is a limit [in adapting to minority demands] beyond which a democratic host society cannot go without losing its identity.

Here, Here. Immigration must not be allowed to become colonization, in Australia or in the United States. By any group.