There has been research done about personality factors and spiritual experience.

There is an interesting researcher who discovered a personality trait by studying those prone to nightmares. His name is Ernest Hartman and the his theory is about thin and thick boundary types. Thin boundary types are more likely to suffer nightmares and to remember dreams because the boundary between waking and dreaming is thinner. Also, thin boundary types are more likely to believe in the supernatural and more likely to claim to have had experiences of the supernatural.

Other researchers have studied boundary types as they relate to various personality theories. In terms of MBTI, thin boundary types correlate with N, F, and P. Here are two links that discuss this:

Personality and Motivations to Believe, Misbelieve, and Disbelieve in Paranormal Phenomena