But is it actually a doctrinal prohibition, or merely an evolved tradition? Early Saints aggressively distanced themselves from the Cross to show distinct separation from the other Christian denominations. But more recently, remarks by the late President Gordon B. Hinckley suggest that it is merely a tradition rather than a hard core doctrine. Some of his remarks were recorded in the September 1996 edition of the New Era magazine, and LDS publication tailored towards adolescent Mormons. Here's the pertinent part of the article:
“Q&A: Questions and Answers,” New Era, Sep 1996, 17
Answers are intended for help and perspective, NOT as pronouncements of Church doctrine.
Question: I have a friend who is a member of another religion and who asked me why we don’t wear crosses or have crosses on our buildings. Why don’t we?
New Era Answer: We do not use the cross as a symbol on our chapels, temples, or on our scriptures or in jewelry. President Gordon B. Hinckley explained the reason in a talk delivered in general conference. He told about talking to a Protestant minister following a temple open house. The minister had asked why there were no crosses anywhere if we say we believe in Jesus Christ. President Hinckley answered, “ ‘I do not wish to give offense to any of my Christian brethren who use the cross on the steeples of their cathedrals and at the altars of their chapels, who wear it on their vestments, and imprint it on their books and other literature. But for us, the cross is the symbol of the dying Christ, while our message is a declaration of the living Christ.’"
“He then asked, ‘If you do not use the cross, what is the symbol of your religion?’ I replied that the lives of our people must become the only meaningful expression of our faith and, in fact, therefore, the symbol of our worship” (“The Symbol of Christ,” New Era, Apr. 1990, p. 4).
President Hinckley further explained, “On Calvary he was the dying Jesus. From the tomb he emerged the living Christ. … Because our Savior lives, we do not use the symbol of his death as the symbol of our faith. But what shall we use? No sign, no work of art, no representation of form is adequate to express the glory and the wonder of the Living Christ. He told us what that symbol should be when he said, ‘If ye love me, keep my commandments’ (John 14:15)” (pp. 6, 7).
Even though we do not believe in using the cross as a symbol in our Church, we do not criticize others for wearing or using the cross in their religions. We should understand that the cross is significant and sacred to them. In fact, the 11th article of faith says, “We claim the privilege of worshiping Almighty God according to the dictates of our own conscience, and allow all men the same privilege, let them worship how, where, or what they may.”
We focus on the great atonement of our Savior, his sacrifice for us that makes eternal life possible. We think of his life and sacrifice every Sunday during the sacrament. Our testimonies become the precious things that we bear, along with our obedience, to show we are true followers of Christ.
The bottom line - while the mission of Jesus Christ required the agony of taking upon Himself all of the world's sins at Gethsemane and offering Himself as a substitutionary sacrifice at Calvary in order to gain the authority to take up His own body in the Resurrection to deliver us from eternal separation from the Father and spiritual death, it is the Resurrection that frees all of us, and so we choose to focus upon that final act. Thus we honor the Resurrected Christ over the Crucified Christ. But what we strive for is that instead of displaying external symbols of Christ, each Latter-day Saint becomes a living symbol of Jesus Christ by personal example.
Another reason why we tend to downplay the Cross is that many Latter-day Saints believe that the Cross has become excessively commodified and marketed in the secular world. Consequently, we do not wish to contribute further to that commodification. Some interesting further discussion available on a 2006 post on Feminist Mormon Housewives, a July 2008 post on AnsweringTheCritics, and a January 2009 post on Mormon Matters.
But as President Hinckley pointed out, we are NOT to look down upon our fellow Christians who do choose to use the Cross as a symbol of worship, just as we are not to belittle Catholics for paying appropriate honor to Mary, the earthly Mother of Christ. When we do belittle our fellow Christians for adhering to different traditions that have no bearing upon us, we are engaging in Pharisaism. Jesus Christ was a victim of Pharisaism; while the Romans executed the death sentence upon Jesus, it was the Pharisees and Saduccees who assembled themselves before Pontius Pilate, and screamed "Release Barrabas!" "Crucify Jesus!" The Romans were merely professionals obeying orders; it was the Pharisees who actually thirsted for Christ's blood (although we cannot say for certain whether or not they will end up as sons of perdition).