The cross is not used by other religions as a result of a commandment by God. In fact, there is not one scripture that can even be construed as to mean that the true church of God would use a cross as its symbol of its belief in Christ. Of course, the scriptures wouldn't speak of "mainstream" Christianity versus non-"mainstream" Christianity because in the scriptures there are only two major churches -- the Church of Christ and the Church of the devil.
Having explained that, the cross was first used -- get this -- during the Crusades. That's right. It was a symbol of war, not a symbol of religion, per se. So the cross has historical importance in that regard. Over time, because of the aggressive missionary efforts by many churches, the symbol of the cross because the accepted sign of Christianity around the world. What's the trend that you see?
It's all man-made. There's no scriptural basis in the practice. Adam and Eve did not wear a cross in the Garden of Eden, Moses didn't have a cross on his staff, and Jesus certainly did not walk around with a cross around his neck. What you really have conflict with, then, is "mainstream" Christian trends based in historical events that have no scriptural basis. Mormonism simply states that the cross is not an acceptable symbol of our belief in Christ. As Gordon B Hinckley put it, the lives of the members of the Church are the symbol of our belief in Christ.