The Mormons continue to maintain the IGI, so that their members can retrospectively baptize all of their ancestors into their faith. There are special temples allocated to this practice.
It is founded upon the belief that individuals have the opportunity to accept the true teachings of Jesus Christ, regardless of whether they are in this world or the next.
As the Church was only founded in 1830, this leaves a lot of ancestors who may have been Catholic, Protestant or not even Christian during their lives. Their Mormon descendants submit their names as an act of love. Once the priest has performed a baptism-by-proxy on the dead, then the deceased will be able to gain access to Heaven.
Naturally this has caused some outrage amongst other denominations. In 2001, the Vatican's Congregation for the Doctrine of the Faith ruled that Mormon re-baptisms of deceased Catholics could not be held as valid. As far as they are concerned, devout members of the Catholic Church will remain so, regardless of posthumous attempts to incorporate them into another faith.
Nevertheless, the Holy See took the practice seriously enough to wish to hinder Mormons in their family history research. In 2008, the Vatican Congregation for Clergy sent a letter to all of its bishops. It expressly forbade access to Catholic records (birth, marriage and death registers specifically) to any member of the Church of Jesus Christ of Latter-Day Saints.
The idea was to stop Catholics being included on the IGI by refusing to allow Mormons the information necessary to index them. This was a little like slamming the stable gates after the horse has bolted, as hundreds of thousands of them are already on it.
Other religions have been even more proactive in seeking to remove their deceased members from the IGI. In 1994, controversy was sparked when it was discovered that the index included the names of Jews, which had been transcribed from two Holocaust memorial registers. Dying in the death camps for their Judaic faith and heritage, millions of people had now been re-baptized as Mormons.
A year later, an agreement was signed that only Jews who were direct ancestors of living Mormons could be baptized by proxy. Members of JewishGen have continued to monitor the situation and they claim that the promises were not honored. Jews continue to be added to the IGI and re-baptized according to the tenets of the Church of Jesus Christ and the Latter-Day Saints.