Integrated sensing and communication (ISAC) is envisioned as a key technology for future sixth-generation (6G) networks. Classical ISAC system considering monostatic and/or bistatic settings will inevitably degrade both communication and sensing performance due to the limited service coverage and easily blocked transmission paths. Besides, existing ISAC studies usually focus on downlink (DL) or uplink (UL) communication demands and unable to achieve the systematic DL and UL communication tasks. These challenges can be overcome by networked FD ISAC framework. Moreover, ISAC generally considers the trade-off between communication and sensing, unavoidably leading to a loss in communication performance. This shortcoming can be solved by the emerging movable antenna (MA) technology. In this paper, we utilize the MA to promote communication capability with guaranteed sensing performance via jointly designing beamforming, power allocation, receiving filters and MA configuration towards maximizing sum rate. The optimization problem is highly difficult due to the unique channel model deriving from the MA. To resolve this challenge, via leveraging the cutting-the-edge majorization-minimization (MM) method, we develop an efficient solution that optimizes all variables via convex optimization techniques. Extensive simulation results verify the effectiveness of our proposed algorithms and demonstrate the substantial performance promotion by deploying MA in the networked FD ISAC system.