This paper considers the uplink of a cloud radio access network (C-RAN) comprised of several multi-antenna remote radio units (RUs) which send the data that they received from multiple mobile users (MUs) to a central unit (CU) via a wireless fronthaul link. One of the fundamental challenges in implementing C-RAN is the huge data rate required for fronthauling. To address this issue, we employ hybrid radio frequency (RF)/free space optical (FSO) systems for the fronthaul links as they benefit from both the large data rates of FSO links and the reliability of RF links. To efficiently exploit the fronthaul capacity, the RUs employ vector quantization to jointly compress the signals received at their antennas. Moreover, due to the limited available RF spectrum, we assume that the RF multiple-access and fronthaul links employ the same RF resources. Thereby, we propose an adaptive protocol which allocates transmission time to the RF multiple-access and fronthaul links in a time division duplex (TDD) manner and optimizes the quantization noise covariance matrix at each RU such that the sum rate is maximized. Our simulation results reveal that a considerable gain in terms of sum rate can be achieved by the proposed protocol in comparison with benchmark schemes from the literature, especially when the FSO links experience unfavorable atmospheric conditions.