What the public thinks about the Shroud is largely influenced by what journalists write. For the most part they do a reasonable job, usually on a tight deadline after some news item breaks.
Part of the problem is that the Shroud's authenticity seems absurd to many reporters. This is particularly so in light of some of the nuttiness that has been claimed by some enthusiastic believers in its authenticity. Quite often the nuttiness is simply repeated making the problem worse. For instance, there is this quotation from a late 2009 Associated Press (AP) story:
The shroud bears the figure of a crucified man, complete with blood seeping from his hands and feet, and believers say Christ's image was recorded on the linen's fibers at the time of his resurrection.
Who are the believers? People who think the Shroud is authentic? Serious scientific researchers who are studying the images to try and determine how they came to be on the cloth? The public? Those who read the AP story and nonetheless think the Shroud is real? The fact of the matter is that only a few scientists and dedicated researchers who think the Shroud is real--is believers really the right word?--"say" any such thing. The leading hypothesis is that the images were formed by a natural reaction between bodily amino products and a carbohydrate film covering the fibers of the cloth. There is no need to invoke miraculous cause in for such a chemical process. That is what many if not most "believers" think. See: Parsing an Associated Press article by Ariel David
To simply state that believers think this like saying that Christians believe that the world was created in six literal days. Some do. Many if not most Christians do not think so.
The story that includes the above reporting was about an almost certainly flaky claim: that an inscription was found on the Shroud. The reporter did a good job of finding skeptics of the Shroud's authenticity, who were skeptical about the inscription and with good reasons. But what was overlooked was the fact that most people who think the Shroud is authentic agree with the skeptics that the inscription is not there. The story leaves the impression that "believers" think it is there.
Another common problem is the carbon dating. Fortunately, this was addressed correctly in the above mentioned story. Most times, it is not. As with everything about the Shroud, there is a great deal of crazy stuff being said which is reported in the media. It is unfortunate. Nothing is a bigger disservice to readers than to mischaracterize this information. Nothing hampers attempts at arriving at the truth about the Shroud more than characterizing all who think it is real, think that it might be real, or are open-minded as being alike and calling them believers. And this goes for skeptics of authenticity as well, for they are not of one mind either. The number of conflicting explanations for the images and the carbon dating fiasco are difficult to sort out.
If, for instance, we are skeptical about the existence of God or we do not share the belief of many Christians in a physical, bodily resurrection, then it seems very natural be dubious about the authenticity of the Shroud. But it possible for a non-Christian to think the Shroud is authentic. Barrie Schwortz, one of the leading Shroud scholars, is Jewish. He thinks it is real and he thinks so for scientific and historical reasons alone. One of the claims often repeated in the press is that Christians/believers/believers of the Shroud think the images were formed by the Resurrection. The fact of the matter is that there is no evidence in support of such an idea and few serious scientists who study the Shroud think so. The consensus is that the images were formed by some natural phenomenon.
You will read accounts that someone has replicated the image on the Shroud thus showing/proving that it is/could be fake. First of all, no one has done any such thing. It is possible to make something that looks like the image, but unless all image attributes, such as the 3D encoding, are replicated, it has not been done. But beyond that, it is a logical fallacy to think that if the Shroud can be faked the original must also be a fake.
Often, reporters simply state that carbon dating in 1988 showed that the Shroud was medieval. Sometimes you read that scientists/researchers/believers/enthusiasts/fanatics question/disagree with/argue that the carbon dating. Sometimes you will read that they think/suspect/believe that the radiocarbon dating labs used material from a patch. Other reasons are offered as well. A fire in 1532 rejuvenated the cloth making it seem newer than it really was or that a bioplastic film growing on the Shroud distorts the carbon dating or that carbon monoxide can change the carbon dating results or even a conspiracy theory that someone intentionally swapped the samples.
The simple fact is that the material in the carbon dating samples is
chemically unlike the rest of the Shroud. This invalidates the tests.
The best explanation for this difference is that the corner from which
the sample was taken was repaired. It is only a theory but it is
supported by finding cotton fibers, binder, dyestuff and splices in the
sample area. These things do not exist elsewhere on the Shroud. All of
this is reported in a peer-reviewed paper in a scientific journal. Some
of the findings have been confirmed by a materials chemist at Georgia
Tech and a team of nine scientists at the Los Alamos National Laboratory
in New Mexico.