There are two statements today from the Church.
10 June 2011 — Salt Lake City
The Church of Jesus Christ of Latter-day Saints today issued the following official statement on immigration:
Around the world, debate on the immigration question has become intense. That is especially so in the United States. Most Americans agree that the federal government of the United States should secure its borders and sharply reduce or eliminate the flow of undocumented immigrants. Unchecked and unregulated, such a flow may destabilize society and ultimately become unsustainable.
As a matter of policy, The Church of Jesus Christ of Latter-day Saints discourages its members from entering any country without legal documentation, and from deliberately overstaying legal travel visas.
What to do with the estimated 12 million undocumented immigrants now residing in various states within the United States is the biggest challenge in the immigration debate. The bedrock moral issue for The Church of Jesus Christ of Latter-day Saints is how we treat each other as children of God.
The history of mass expulsion or mistreatment of individuals or families is cause for concern especially where race, culture, or religion are involved. This should give pause to any policy that contemplates targeting any one group, particularly if that group comes mostly from one heritage.
As those on all sides of the immigration debate in the United States have noted, this issue is one that must ultimately be resolved by the federal government.
The Church of Jesus Christ of Latter-day Saints is concerned that any state legislation that only contains enforcement provisions is likely to fall short of the high moral standard of treating each other as children of God.
The Church supports an approach where undocumented immigrants are allowed to square themselves with the law and continue to work without this necessarily leading to citizenship.
In furtherance of needed immigration reform in the United States, The Church of Jesus Christ of Latter-day Saints supports a balanced and civil approach to a challenging problem, fully consistent with its tradition of compassion, its reverence for family, and its commitment to law.
There was also this:
Responsibility of Church Members: Avoiding Being Judgmental
10 June 2011 — Salt Lake City
The First Presidency has for many years taught that undocumented status should not by itself prevent an otherwise worthy Church member from entering the temple or being ordained to the priesthood.
Bishops are in the best position to make appropriate judgments as to Church privileges. Meanwhile, Church members should avoid making judgments about fellow members in their congregations.