I really didn't see reports showing these possibilities of damages from projector usage. Projectors would give out strong light. Strong light might make eyes very uncomfortable and even hurt. If you don't look directly at the machine, it should be no problem, after all people don't have to look at the strong light source to use this machine. No matter what you are looking at, it requires a focusing power. So don't look at the same object with same distance, otherwise your eyes will be tired. Good habit of using eyes is the best way to protect your eyes.
Currently the digital projector's light source is usually 6 kilowatt's xenon lamp, which the human being's eyes would not accept. So please do not directly stare at the light source. But the instant shinning will be no such big problem with your eyes. However, the big screen will need strong light source, and if the dark/bright contrast is too differing from each other, these reasons will cause the discomfortable with your eyes. Moreover, all the electrical devices may affect the eyes in certain extents. You can choose the project with suitable light intensity for yourself. Please do not consider the too much dark or bright one will be good to your eyes, the most comfortable one will be the best for you. So please follow your nose to buy.