Religious reasons aside, the Shroud of Turin is capitalized because it is a proper noun, it is no different than capitalizing the Arch of Titus in Rome or the Brooklyn Bridge.
Good grief. Are we to worship a piece of hemp or flax? Are we to show "respect" through punctuation? Are we to kiss the leather of a sandal or even the blanket that swaddled the Christ child?
God forbid such idolatry.
"Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things. Wherefore God also gave them up to uncleanness through the lusts of their own hearts, to dishonour their own bodies between themselves: Who changed the truth of God into a lie, and worshipped and served the creature more than the Creator, who is blessed for ever. Amen." -- Romans 1:21-25
"Wherefore if ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances, (Touch not; taste not; handle not; 2 Which all are to perish with the using;) after the commandments and doctrines of men?" -- Colossians 2:20-22"Kiss the Son, lest he be angry, and ye perish from the way, when his wrath is kindled but a little. Blessed are all they that put their trust in him." -- Psalms 2:12
Get it? The reality of our sanctified life is spiritual, not physical "after the commandments and doctrines of men."
Christ told us the only "sign" we need is His resurrection. To look for more, especially in the physical world, shows a lack of trust in Him and His word.