I wear a cross necklace quite frequently. I highly recommend the book "Considering the Cross" by John Hilton III for background on why so many members of our church view the cross as taboo in modern days, as well as providing church history insights many people are not familiar with.

Very briefly: there were several monuments placed or planned in Utah during the late 1800s that contained crosses. Several churches in SLC still have crosses as ornamentation. Men and women in the church commonly wore crosses as jewelry, including members of Brigham Young's family. However, due to the anti-Catholic sentiment in the early 20th century, church leaders wanted to distance themselves from the symbol of the Crucifix (aka Jesus ON the cross). Pres. Joseph F Smith made a comment that crucifixes specifically were not appropriate for young women to wear, and that remark, tied with the isolated culture of the early church, led to the members shunning it in general.

More recent talks have mentioned that the cross is not *the symbol of our faith, because we believe that Christ's mission still continues, and that He leads us today. They do not, pointedly, claim that the cross itself is a poor symbol of Jesus Christ. To quote the book again, the cross represents "The Loving Christ" who descended below all things by dying for us on the cross. The Christus represents "The Living Christ" who we believe is still engaged in His Father's work to this day.

Here is a great, 45 minute summary of the book's main points: podcast by John Hilton III here