This work studies the uplink of a multi-tenant cloud radio access network (C-RAN) system with spectrum pooling. In the system, each operator has a cloud processor (CP) connected to a set of proprietary radio units (RUs) through finite-capacity fronthaul links. The uplink spectrum is divided into private and shared subbands, and all the user equipments (UEs) of the participating operators can simultaneously transmit signals on the shared subband. To mitigate inter-operator interference on the shared subband, the CPs of the participating operators can exchange compressed uplink baseband signals on finite-capacity backhaul links. This work tackles the problem of jointly optimizing bandwidth allocation, transmit power control and fronthaul compression strategies. In the optimization, we impose that the inter-operator privacy loss be limited by a given threshold value. An iterative algorithm is proposed to find a suboptimal solution based on the matrix fractional programming approach. Numerical results validate the advantages of the proposed optimized spectrum pooling scheme.