The notion of a “Church without border” may be alarming, bothersome, or a head scratcher to many Christians, even many Catholics. But the bishops south of the US advocate a connection across political borders, and that presumably means dioceses in the States:
413. To attain this objective, dialogue between the sending and receiving churches must be enhanced so as to provide humanitarian and pastoral care to those who have moved, supporting them in their religiosity, and appreciating their cultural expressions in everything having to do with the Gospel.
Seminary formation must attend to the issues:
Awareness of the reality of human mobility must be developed in seminaries and houses of formation so as to provide a pastoral response to it.
And lay people, not only for religious education, but also for our role among the secular structures of the world:
Likewise attention must be given to preparing lay people who with a Christian sense, professional competence, and capacity for understanding, can accompany those arriving, and likewise the families left behind in their places of origin.(Cf. EMCC. 70, 71, and 86-88)
Pope Benedict XVI chooses to look on the bright side:
We think that “the reality of migrations must never been seen as a problem, but rather and particularly as a great resource for the journey of humankind.”(Benedict XVI, Address, Angelus, January 14, 2007)
People on the move are a rich source of inter-cultural understanding and fertilization. Without migrants, we become inbred and stagnant in a number of ways.
For deeper examination, an English translation of the 2007 document from the Aparecida Conference.