I would think that many people interested in the Shroud of Turin would be very skeptical about radiocarbon dating, since for one thing that indicates that the Earth is billions of years old.
If you are of the sort who believes that the earth is mere thousands of years old and God put fossils, geological strata, etc. in the ground to challenge the faith of Atheists, you are welcome to believe whatever you like regarding the Shroud of Turin, and little things like evidence and science will likely not get in your way.