No more than printed materials
Cathode ray monitors (with a bulky cathode ray tube at the back) could theoretically harm vision, as the impact of electrons on the phosphor layer generates slight X-ray radiation.
Special protective measures were provided for such screens. However, these monitors are now practically obsolete, and they were never used in portable devices.
Modern liquid crystal displays emit nothing but visible light, and the eyes can become fatigued when working with them just as they can when reading books, for example.
