When Mormons are given their garments they are (unless it has changed) told the garments are “a shield, and a protection.” That is also found in the Missionary Handbook. I knew some Mormons who told me that the protection was a protection from temptation. I don’t know how that was supposed to work. But they said the devil more easily succeeds in his efforts to sway ungarmented people. The official Church Handbook of Instructions said the temple garment “provides protection against temptation and evil.” If it protects against “evil” then it either prevents the wearer from committing evil or it prevents evil from affecting the wearer. “If respected and honored, the garment protects us from temptations and unrighteous influences.” (Kent F. Richards, Executive Director of the Temple Department, July 2015)
Past prophet Spencer Kimball said that there "undoubtedly have been many cases where there has been, through faith, an actual physical protection, so we must not minimize that possibility.” When Joseph Smith was killed, one man who survived credited his temple garments for his physical survival. For some reason Smith and others had removed their garments, but I have no idea why they would have done that.
Historically, Mormons (some at least) believed Satan was almost at their side waiting to take control of them if they dared remove their “garments.” Those people would only remove part of their garment at a time, for example, leaving one arm in, while they bated, and then after putting the garment back on, removing the sleeve and washing that arm. They put on new garments the same way, removing part of one, putting on the corresponding part of the other, and so on, till they had exchanged their garments without ever having been complete out of either one.
Moonies also have had protective items. Originally a photo of their leader Sun Myung Moon, at one time it was a photo of his deceased son, but I haven’t heard of anything other than those for quite a while even though I have a acquaintances among them.