An electronic device may have a display. Inactive portions of the display may be masked using an opaque masking layer. An opening may be provided in the masking layer. A camera may receive light through the opening in the opaque masking layer. The display may include upper and lower polarizers, a color filter layer, and a thin-film transistor layer. The upper polarizer may have an unpolarized window aligned with the opening in the opaque masking layer for the camera, a logo, or another internal structure. The unpolarized window may be formed from openings in polarizer layers such as a polyvinyl alcohol layer and optical retarder layers. The openings may pass through all or less than all of the polarizer layers. The openings may be filled with transparent filler material. The polarizer may include a try-acetyl cellulose layer that continuously covers the opening in other polarizer layers.