This is a pretty strange claim to me. I definitely agree there are some religious strands that are anti-intellectual. But then there are Augustine, Ambrose, Thomas Aquinas, John Calvin, Francis Turretin, John Owen, etc., whose works most people are simply incapable of grasping, and fewer still can equal. Many of us are trained with these intellectual giants to show us not what, but how, to think.
Are you aware of these great thinkers and their contributions to your thought life?
To pick a random example among many, our concept of personhood relies heavily on a theologian named Turtullian, before whom person (Latin, "persona") merely meant an actor's mask (i.e, the role one plays). Tertullian explored the enduring "substance" of a person, regardless of what role they play in life -- concepts we now assume as a given, but were hotly contested at the time.
Religious upbringing or being indoctrinated into not thinking for yourself as a child is probably a likely reason people turn to things such as psychics.