As a continuation of the conversation below, I thought it might be helpful to point out that the Catholic Church didn't suddenly discover the immigration issue in a fit of political correctness after the Second Vatican Council.
Pope Pius XII's Exsul Familia Nazarethena summarizes the Catholic position here beautifully:
"The natural law itself, no less than devotion to humanity, urges that ways of migration be opened to these people. For the Creator of the universe made all good things primarily for the good of all. Since land everywhere offers the possibility of supporting a large number of people, the sovereignty of the State, although it must be respected, cannot be exaggerated to the point that access to this land is, for inadequate or unjustified reasons, denied to needy and decent people from other nations, provided of course, that the public wealth, considered very carefully, does not forbid this."
The "natural law itself" urges that migrants and refugees be accommodated, considering that "the public wealth" does not forbid it. How "the public wealth" is defined and measured is bound to be hotly debated, but for Catholics that debate will be informed by traditional principles of justice and charity as applied to the common good, and will not neglect to safeguard the interests of the Catholic religion and its adherents.
The document is quite long, so I've pasted a few more relevant excerpts:
The émigré Holy Family of Nazareth, fleeing into Egypt, is the archetype of every refugee family. Jesus, Mary and Joseph, living in exile in Egypt to escape the fury of an evil king, are, for all times and all places, the models and protectors of every migrant, alien and refugee of whatever kind who, whether compelled by fear of persecution or by want, is forced to leave his native land, his beloved parents and relatives, his close friends, and to seek a foreign soil.
For the almighty and most merciful God decreed that His only Son, "being made like unto men and appearing in the form of a man," should, together with His Immaculate Virgin Mother and His holy guardian Joseph, be in this type too of hardship and grief, the firstborn among many brethren, and precede them in it.
We have tried earnestly to produce in the minds of all people a sympathetic approach towards exiles and refugees who are our needier brothers. In fact, we have often spoken of their wretched lives, upheld their rights, and more than once appealed in their behalf to the generosity of all men and especially of Catholics. This we have done in radio addresses, in talks and discourses given as occasion arose, and in letters to archbishops and bishops.
We wrote, for example, to our Venerable Brothers, Archbishops, Bishops and Ordinaries of places in Germany:
In the present circumstances, what seems most likely to stimulate and heighten your own charity and that of the German clergy is the necessity of assisting refugees by every resource and means of your ministry. We refer both to refugees from your land who live abroad in scattered regions and to alien refugees in Germany who, often deprived of their friends, their goods and their homes, are forced to lead a squalid and forlorn existence, usually in barracks outside the towns. May all good Germans and especially the priests and members of Catholic Action, turn their eyes and hearts toward these suffering neighbors and provide them with everything required by religion and charity.
Similarly, in our Encyclical Redemptoris Nostri on the Holy Places in Palestine, we lamented sadly:
Very many fugitives of all ages and every state of life, driven abroad by the disastrous war, cry pitifully to us. They live in exile, under guard, and exposed to disease and all manner of dangers.
We are not unaware of the great contributions of public bodies and private citizens to the relief of this stricken multitude; and we, in a continuation of those efforts of charity with which we began our Pontificate, have truly done all in our power to relieve the greatest needs of these millions.
But the condition of these exiles is indeed so critical, so unstable that it cannot lot much longer. Therefore, since it is our duty to urge all generous and well-minded souls to relieve as much as possible the wretchedness and want of these exiles, we most earnestly implore those in authority to do justice to all who have been driven far away from homes by the tempest of war and who long above all to live in quiet once more.
Moreover, we have repeatedly addressed the Rulers of States, the heads of agencies, and all upright and cooperative men, urging upon them the need to consider and resolve the very serious problems of refugees and migrants, and, at the same time, to think of the heavy burdens which all peoples bear because of the war and the specific means that should be applied to alleviate the grave evils. We asked them also to consider how beneficial for humanity it would be if cooperative and joint efforts would relieve, promptly and effectively, the urgent needs of the sufferings, by harmonizing the requirements of justice with needs of charity. Relief alone can remedy, to a certain extent, many unjust social conditions. But we know that this is not sufficient. In the first place, there must be justice, which should prevail and be put into practice.
Our planet, with all its extent of oceans and was and lakes, with mountains and plains covered with eternal snows and ice, with great deserts and traceless lands, is not, at the same time, without habitable regions and living spaces now abandoned to wild natural vegetation and well suited to be cultivated by man to satisfy his needs and civil activities: and more than once, it is inevitable that some families migrating from one spot to another should go elsewhere in search of a new home-land.
Then,—according to the teaching of “Rerum Novarum,” —the right of the family to a living space is recognized. When this happens, migration attains its natural scope as experience often shows. We mean, the more favorable distribution of men on the earth's surface suitable to colonies of agricultural workers; that surface which God created and prepared for the use of all.
If the two parties, those who agree to leave their native land and those who agree to admit the newcomers, remain anxious to eliminate as far as possible all obstacles to the birth and growth of real confidence between the country of emigration and that of immigration, all those affected by such transference of people and places will profit by the transaction.
The families will receive a plot of ground which will be native for them in the true sense of the ward; the thickly inhabited countries will he relieved and their people will acquire new friends in foreign countries; and the States which receive the emigrants will acquire industrious citizens. In this way, the nations which give and those which receive will both contribute to the increased welfare of man and the progress of human culture.