An electronic device display may have an organic light-emitting diode layer that emits light to form images for a user. Reflective structures such as metal signal lines may be present in the organic light-emitting diode layer. Ambient light reflections from the metal signal lines may be suppressed using a circular polarizer on the organic light-emitting diode layer. To increase light emission efficiency from the organic light-emitting diode display layer under low ambient light conditions in which ambient light reflections are not significant, the polarization efficiency of the circular polarizer may be reduced. Control circuitry may make measurements of ambient light intensity using an ambient light sensor and can control the polarization efficiency of the circular polarizer accordingly by applying adjustable amounts of light or electric field. Polarization efficiency may also be adjusted using a photosensitive polarizer material that responds directly to changes in ambient light level.