The two threads have been co-mingled
For centuries, this "icon" has been used as support of the "reality" of the Christian religion, and is interwoven into the history of the church. If you cut one thread, you weaken others.
If the Shroud is disproven, there will be some collateral damage, just as ALL "cryptozooology" was damaged by last week's stupid Bigfoot fraud.
imho...