There is no need for a conspiracy to explain why the Christ Myth Theory is excluded from public sight, any more than people in the Middle Ages conspired to assert the earth was flat. Ignorant people just assume their belief is true and ignore anyone who thinks differently, especially when the belief is important for their religion. Many believers regard questioning the historical existence of Jesus Christ as personally offensive.
Let's go back to Ant's famous three criteria:
1. Independent attestation - (maintains that traditions that are attested independently by more than one source are more likely to be reliable than those found in only one source.)
There is none. As I linked before, and as Ant ignored, Church Fathers discussed the very section of writing by Josephus which presents the only claimed first century independent attestation of Christ, but they did not notice the famous mention of Jesus, even though they would have been all over it like a rash if it were there. This "attestation" was not added for three hundred years, and the reason Eusebius forged the Josephus text about Jesus was simply because it was so very embarrassing for church liars that they had no independent attestation for this guy who was supposedly famed far and wide, publicly crucified as King of the Jews, etc ad pukem.
The Gospels are not independent of each other, any more than various different books by L Ron Hubbard and his acolytes or by the Mormon Church are independent of each other.
By contrast, Plato is completely independent of Aristophanes as contemporary attestation of Socrates. Nothing remotely comparable exists for Jesus. Put that in your pipe and smoke it.
criterion of dissimilarity - traditions that appear to work against the vested interests of the Christians who were telling them are more likely to be historically accurate than those that Christians may have “made up” to suit their own purposes.
This argument was used by Christopher Hitchens to say that he found it incredible that the Gospels include stories that some might think put Jesus in a less than perfect light, and that these texts are evidence that Jesus existed. They are nothing of the sort.
Sir Lancelot of the Lake has an extensive legend of his madness, but that is not evidence for Lancelot any more than the madness of Don Quixote is evidence for historicity. The stated objective of the story of Jesus is to encourage belief. As such, quirky details add to his humanity. People can relate to a character who is unpredictable. This criterion is garbage as far as any real historical evidence is concerned.
But there is one sense in which this criterion is true. Eusebius was a Liar for the Lord. Revealing this deception is against the vested interest of the church, but is obviously historically accurate.
criterion of contextual credibility - argues that no tradition about Jesus can be accepted as reliable if it cannot plausibly be situated in a first-century Jewish Palestinian context
In that case you have to junk the whole New Testament on grounds of implausibility. It refers to Nazareth, which did not exist when Jesus lived. Paul never mentions any geographical location for Jesus. The context Paul provides is mythic, not historical.
Now Ant, you have cited these criteria as supposedly supportive of the Historical Jesus hypothesis. In fact, they support the Christ Myth hypothesis. The decisive fact is that Christianity was generated by a cult, just like Scientology or Mormonism. We know both of those are entirely fictional, but are somehow emotionally attractive to large numbers of otherwise intelligent people. Even Mitt Romney looks shifty and implies that hey everyone believes kooky things when pressed (or so I am told).
Sadly, scholarly research about Jesus is mostly far from rigorous. People who have grown up in a cult where JC was their bestest friend are brainwashed, and they bring this rinse cycle in at the foundation of their research, as an assumption that they do not question. They also know that universities and theological colleges are corrupt, and that anyone who is honest about the real evidence on Jesus has little hope of career advancement, so they internalise the prejudices of the community.