Robin Emmott of Reuters says:

Weary migrants on their journey north often recharge their batteries at a network of [Catholic Church operated] shelters run by the Roman Catholic Church -- a lifeline sanctioned by the Vatican, despite increased U.S. efforts to keep out illegal immigrants.

"Migration is a human right and migrants are some of the world's most vulnerable people. It is the church's obligation to help them," said the Rev. Francisco Pellizzari, an Italian-Argentine missionary who runs the Nazareth migrant shelter in Nuevo Laredo.

...The Nuevo Laredo shelter has been granted a papal blessing in a Vatican certificate that hangs proudly on the wall.

...The church denies any wrongdoing and says it is stepping in to fill the void created by the lack of a U.S. immigration policy and the failure of Latin American countries to create more jobs for their people.

"While the governments of the United States and Latin America fail to provide workable policies, the church will do what it must to help the migrant," said Rafael Romo, Archbishop of Tijuana on Mexico's border with California. "We can't let these people be treated like animals."

It's apparently too complicated for them to consider feeding people and then encouraging them not to cross the border and, instead of concentrating on assisting illegal immigration concentrating on encouraging reforms in Mexico and other countries. The article does point out that, oddly enough, millions of illegal aliens from Latin America have done wonders for church attendance in the U.S. Note also that Church activities in Mexico are more circumscribed than they are here (example).