Well, eventually it’s no longer a matter of process, but substance.
Should the scientific team have to tolerate a “skeptic” who ignores the evidence that the team has gathered, because he is PHILOSOPHICALLY committed to denying the reality of that evidence? Especially if he is noisily obnoxious about it.
Since the Shroud research has always been published, the public can decide.
That’s an entirely different matter from the exclusion, by thugs, of “climate skeptics” from Vatican meetings. The Vatican isn’t conducting any “research” or publishing any scientific findings. They are just conducting propaganda rallies.
That's part of the problem. They are often hard to find, while on the other hand discussion about them (and what they purport to have found) abound.
When digging through the papers of one (I can't recall exactly which now, there are so many twists and turns in regards to claims and counter-claims it is difficult to keep track) they went on and on about how a testing process functioned --- then pronounced that whatever they were testing of the shroud fit the bill- yet that ending result pronouncement coming suddenly & awkwardly before the run-down description of the theory of how such testing is to be conducted again commenced.
Everything else about the thing, if there is some type of doubt which skeptics can point towards has had evolved over a period of time extensively complex explanations which often (at crucial junctions) rely upon an alleged researcher's own word, or else for example, as in the instance of pollen grain discussion rely upon interpretive analysis -- which can leave other experts of the same field scratching their heads, asking how in the...? can anyone come up with THAT sort of exactitude? That cannot be determined by visual analysis alone (or so yet another pollen expert said). Yet that exactitude was the whole point, and without it pollen grain analysis as some form of proof is otherwise worthless.
That the materials available for testing have been so severely limited rendering most things to not be repeatable, so far ---leaves them less than scientific, even in regards to the carbon14 samples from the alleged to have been "repaired with invisible weaving" portion. There too we must rely upon pro-authentication shroud enthusiast scientist who make claims ---yet without showing us actual sample of how they arrived at the conclusions which they did. An s twist around a z twist. Oh really? Then why not provide documentary photographic evidence or having whatever finding it was either verified by multiple dis-interested witnesses, or else if lab testing be duplicated by yet someone else using double-blind sort of materials submission with no one but an assembly of both enthusiasts and skeptics knowing the keys to what materials were what.
That said, I would like to consider the shroud to be the burial cloths, but see no real need.
At the least the subject matter would get people who otherwise not think of Jesus Christ all that much, to think of the tomb it was written of that he was laid in, after death (no "swooning" as per Muslim description, or else some substitute victim not Jesus but a look-alike as some of their stories about Jesus go) and that this same body-- the same exact person otherwise known to have been born of Mary and all the rest which the NT Scriptures detail of his life --- miraculously resurrected after death.