That is what we teach with Baptism, and with the Temple! Thats the reason why clothing is part of it. It is to show we are worthy, that we are clean. (This is the same lesson that can apply to a deacon, or anybody in the Aaronic Priesthood)
As Elder Oaks brought up in the last General Conference.
Elder Jeffrey R. Holland gave a valuable teaching on this subject in general conference 13 years ago. Since most of our current deacons were not even born when these words were last spoken here, I repeat them for their benefit and that of their parents and teachers: “May I suggest that wherever possible a white shirt be worn by the deacons, teachers, and priests who handle the sacrament. For sacred ordinances in the Church we often use ceremonial clothing, and a white shirt could be seen as a gentle reminder of the white clothing you wore in the baptismal font and an anticipation of the white shirt you will soon wear into the temple and onto your missions†(“This Do in Remembrance of Me,†Ensign, Nov. 1995, 68).