In the case of the shroud, belief without basis is not necessary. The thing is basically a photographic negative created at a time prior to photography being invented on the planet...
Also, it is a 3-D image - something that could not be faked.
To this day no one has ever been able to reproduce a similar relic with all of modern science at their disposal.
To paraphrase a StarTrek line....
“It’s real, Jim”