Do you remember the Magic Eye illusions from when you were a kid? In these illusions, you see what looks like a random pattern of colors on a page; if you cross your eyes or stare long enough, you can see the illusion of a 3-D image in the middle of the page. Scientists call these images Random Dot Stereograms. Typically when we look at a 3-D scene, our left eye sees an image that is slightly different from what our right eye sees. We line up those two images to get a 3-D view of the world. This is called stereopsis. Random Dot Stereograms trick our perceptual systems into lining up two parts of the pattern with our eyes, and thus create the illusion of depth. Children are significantly better than adults at seeing these illusions. They are also much faster. This difference may be because children are better at crossing their eyes while keeping a pattern in focus.

From what I can tell, scientists haven't looked at the effect of personal relevance on the speed at which someone sees an illusion, but it could be a great science fair project!

Reference: Dowd, J. M., Clifton, R. K., Anderson, D. R., Eichelman, W. H. (1980). Children perceive large-disparity random-dot stereograms more readily than adults. Journal of Experimental Child Psychology, 29(1), 1-11.