I shall copy a few quotes from The Guardian:
"According to Time magazine, the US charity's work has included training chaplains for the rightwing contra rebels in Nicaragua and sending thousands of Arabic versions of the New Testament into Saudi Arabia during the Gulf war. Last year, the charity was criticised in a New York Times article for holding prayer sessions in several villages in El Salvador before showing residents how to build emergency shelters following an earthquake. "
"At Save the Children, Brendan Paddy acknowledges that many Christian-based humanitarian agencies, such as Christian Aid and Cafod, and even evangelical charities such as the Tear Fund, are well-regarded. "They demonstrate their religious values through their actions," he says.
However, he questions the economic sense of shipping boxes full of donated goods, arguing that transport costs could make the items more expensive than they would be in the recipient country. "Also, because each box contains different items, that can create conflict among the recipients," he says, stressing that a key principle of emergency relief was equality.
In many ways, says Paddy, appeals such as Operation Christmas Child are "something that benefits the giver more than the receiver".
"However, SPI's website features links to a Samaritan's Purse newsletter from Graham, in which he states that God has blessed Operation Christmas Child "because it is about more than Christmas presents". He says: "It is about introducing children and their families to God's greatest gift - His Son, Jesus Christ. As long as evangelism is the focus, God will continue to bless it."
The newsletter says the boxes are distributed along with evangelical literature and that the boxes "have led to salvation for tens of thousands of children and their families". It cites examples such as in Zambia, where "one shoebox prepared the way for nearly two dozen people to come to faith in Jesus Christ".
Follow-up materials "give children further opportunities to accept Christ and grow in their faith". Hundreds of thousands of children in developing countries are said to have participated in a 10-lesson Bible-study course run by the charity."
I think those quotes cover nearly everything discussed on the thread so far.