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Question: Do Mormons believe that the temple garment will protect them from physical harm?
Question: Do Latter-day Saints believe that the temple garment will protect them from physical harm?
The 'protection' of the garment is spiritual, not physical
The First Presidency of the LDS Church has explained in plain terms that the temple garment serves as "a protection against temptation and evil" and instead of it being some type of 'lucky talisman' the "promise of protection [associated with it] is conditioned upon worthiness and faithfulness." (First Presidency Letter, 10 October 1988; see Ensign, August 1997, 19-).
Elder Boyd K. Packer of the Quorum of the Twelve Apostles has published a similar view about the kind of protection that is provided by the temple garment. He said that it "fosters modesty and becomes a shield and a protection to the wearer. . . . For many Church members the garment has formed a barrier of protection when the wearer has been faced with temptation." 
Elder Russell M. Nelson of the Twelve has said -- using symbolic language -- that "we wear the [temple] garment faithfully as part of the enduring armor of God." (Ensign, May 2001, 32-). Spiritual 'armor' is certainly designed to give a person spiritual protection, not to prevent numerous forms of physical harm.
- Boyd K. Packer, The Holy Temple (Salt Lake City: Bookcraft, 1980), 75ff.