Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments in these areas. To date, Bell tests have relied on careful calibration of the measurement devices and alignment of a shared reference frame between the two parties---both technically demanding tasks in general. Surprisingly, we show that neither of these operations are necessary, violating Bell inequalities with near certainty with (i) unaligned, but calibrated, measurement devices, and (ii) uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen local measurements on a singlet state of two photons implemented with reconfigurable integrated optical waveguide circuits based on voltage-controlled phase shifters. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This new approach is likely to have important applications in both fundamental science and in quantum technologies, including device independent quantum key distribution.