The Templars were such a mysterious organisation with so many unanswered questions that they can be used to fill any gap that has some form of mystery linked to it. They themselves had an obsession with secrecy making it very difficult for historians to place all of the pieces of the puzzle together. With such a lack of available information it’s easy to assume they had a hidden agenda.
In other words, be careful. I have long believed that they may have known about the Shroud but I see no reasonable history to support the idea that they had anything to do with it.