What is the difference between "faith" and "gullibility"? The same thing that war is good for: absolutely nothing ("Good God, Y'all").
Let's define some terms:
Gullibility: tendency to believe too readily and therefore to be easily deceived. Noun: credulity, innocence, naïveté, blind faith, credulousness, simplicity. "She must take part of the blame for her own gullibility".
Faith: 1. Confident belief in the truth, value, or trustworthiness of a person, idea, or thing. Strong or unshakable belief in something, esp without proof or evidence. Noun: confidence, trust, credit, conviction, assurance, dependence, reliance, credence. "She had placed a great deal of faith in him".
Upon reading the above definitions, I hope you noticed that the only real difference between the words "faith" and "gullibility" is the connotation that "gullibility" is inherently negative, and therefore, undesirable. Keep this in mind as I attempt to show that the two words are essentially the same in meaning.
John chapter 20 is the story of the resurrection of Jesus and his subsequent appearances to various people, including the infamous Doubting Thomas (aka "Didymus"). Famously, after Thomas put his fingers in Jesus's side and felt his wounds to verify that the man before him was, in fact, the resurrected Christ, Jesus is quoted as saying to Thomas:
"Thomas, because thou hast seen me, thou hast believed: blessed are they that have not seen, and yet have believed."
Here Jesus is setting the standard that believing the testimony of other people is a valid reason to believe a given claim, and is seemingly more favorable in the eyes of god than withholding belief until one can verify the claim through empiricism and evidence. In other words, taking some one's word for something is just as good--if not better--than actually experiencing it firsthand. God will allegedly bless those who believe without good reasons to do so.
As absurd as this sounds, it is reinforced again in the Book of Mormon as Jesus appears to the Nephites in 3 Nephi 11: 14-15. Here Jesus instructs an entire multitude of people to touch his wounds to verify that he is the Christ. In the very next chapter Jesus again affirms that those who believe without seeing him themselves will be blessed.
The thing which strikes me as odd is that both instances are preceded by accounts of people actually seeing Jesus with their own eyes! In the case of Thomas, every single other apostle saw Jesus the week before. The reason he is called "Doubting Thomas" is because he did not believe the outlandish tale of the other apostles that Jesus had resurrected from the dead, without first seeing some evidence. If he had believed them, based only on their word, then he would have rightly been labeled "gullible", because he would have had no reason to accept their extraordinary claim.
As with Thomas, the Nephites who did not actually see and touch Jesus would have no reason to believe such an event had occurred, and would similarly be counted as "believing too readily", thus making them gullible. Would this be commendable or desirable?
Sometimes, critics of Christianity will point these things out to Christians and ask the question, "If Jesus appeared to Doubting Thomas (or the Nephites), why doesn't he appear to people who question his existence today?" This is similar to asking, "Why doesn't god prove his existence to everyone once and for all?" The most common response I have received for asking these types of questions is that if god or Jesus did prove their existence, it would remove the need for faith, and we would all become automatons and robots--devoid of free will, and slaves to our knowledge (or some other nonsensical gibberish).
There are several problems with this argument. For instance, unlike god, I know that police exist; does this knowledge remove my ability to break the law? According to Christian theology, Satan knows that god exists, and yet he continues to rebel. Will we have a perfect knowledge of god's existence in heaven? If so, does this mean there will be no free will in the afterlife, or that we will be angelic slave-bots? Did the apostles (and the Nephites) lose their agency when they saw and touched Jesus?
The proposition of losing free will upon gaining knowledge is unsatisfactory, and does not stand against even the most mild scrutiny. Why then does god not grant all people with knowledge of his existence? Wouldn't withholding information which would save billions of people from experiencing eternal torture implicate the person with that information as being among the most despicable and wretched creatures in existence? Does god get a "pass" here?
Hebrews 11:1 says:
"Now faith is the substance of things hoped for, the evidence of things not seen."
As I understand this passage, faith is hoping for something for which you have no evidence. This is consistent with the definition of "faith" at the top of the page, but the definition provided in the Book of Mormon adds some important information concerning "faith":
"...faith is not to have a perfect knowledge of things; therefore if ye have faith ye hope for things which are not seen, which are true." [emphasis added]
This passage implies that you can only have faith in something which is true. The problem with this is that in order to verify that a given claim is true, you need to provide evidence, which in turn removes the need for faith all together.
For the sake of argument, let's suppose that the accounts of Thomas and the Nephites are true. After having seen and touched Jesus in this way, these people no longer have faith, but knowledge of Jesus's existence. This makes Jesus's comment to Thomas that he should "be not faithless, but believing" nonsensical, since Thomas had empirically confirmed Jesus's existence just moments before.
Believing something to be absolutely true without evidence, however fervently, is a contemptible state of mind. This kind of rationale gives way to holding similarly unjustified beliefs. If you can posit the existence of Bigfoot without evidence, you can equally posit the existence of pixies, Santa Clause, the Flying Spaghetti Monster or Raptor Jesus (see left).
Those who utilize this way of thinking will not be "blessed" as Jesus has twice promised. Rather, it will cloud a mind's ability to make rational decisions, thus making people susceptible to "believing too readily and therefore be easily deceived".
A god which rewards gullibility over rationality is not worthy of worship.
Here is the Atheist Experience discussing Doubting Thomas and gullibility: