Gnostic is about Knowledge, not Belief. What the dictionary says doesn't matter, it merely reflects Usage and not the root Original Meaning of words. Regardless, I'll just agree to disagree on the labels.
No, they are not idiots, but whether they believe or not it has nothing to do with whether Science and Religion are mutually exclusive or not. What makes Science and Religion mutually exclusive is their Method of determining what is True. Religion Believes a set of "Truths", usually based upon Traditions, Holy books, and Dogma. Science assumes nothing, except that the Material world exists, then it investigates that world in order to better understand it.
That is why Religion thought an Earthquake was god's anger at us and Science discovered that Earthquakes were caused by the movement of Tectonic Plates. Or why Religion thought Epileptics were possessed by Demons and Science discovered they had a Medical Condition. The list of contrasts can go on ad infinitum.
There have already been examples of the Religious type in this very thread. At least a couple posters have taken Experiences and merely tacked on religious labels to those experiences. However, even if those experiences were Spiritual Plane induced(exceedingly unlikely, but whatever), they have no sound reason to assume that their particular Religious icons had anything to do with it. They merely experienced a phenomena and applied the labels they are aware of to it. Many of those experiences can be induced in a Lab through changing the chemical balance of the brain and through other stimuli that have no Spiritual connection at all. Many claims by Spiritual people when under Lab conditions have completely failed to work as claimed.