I have thought about this question at length.
I concluded that there were several things that I would need to find (or would at least like to have) in order to reasonably lose my identity as a Christian:
(1) Either a material/psychological explanation for all aspects of possessions/poltergeists or evidence that the methods and rituals used by other religions were equally effective in exorcisms or removing evil spirits from haunted locations. I realize that many possessions/hauntings can probably be explained psychologically, but in the cases where supernatural activity is reported (telekinesis, levitation, hidden knowledge), I'd need a more thorough explanation. I have found several reports that fit my requirements here already, but I'm not sure just how many of them it would take before I considered the amount of evidence to be on par with Christian exorcisms.
(2) Like requirement 1, except in regards to miracles and/or prophecy instead of spirit activity.
(3) Increased knowledge of the reported Canaanite origins of the Abrahamic God. I'd need to know how compelling the evidence is for this. Admittedly, I have very little understanding of it.
(4) A time machine or chronoscope that would allow me to investigate the historicity of the Bible first-hand (ain't gonna happen, but it would be nice...).
Take note that I would not consider the meeting of these requirements to be proof of the absence of a god. A deist interpretation could still work. Nonetheless, I consider the viewpoint of deism, agnosticism and atheism to be nearly the same in a practical sense when it comes to how one conducts their life. I think I'd just be an agnostic until further evidence showed up.