Achieving reliable, cost-effective, and low-carbon energy management for community microgrids (CMs) under suitable computational complexity is challenging due to uncertainties in renewable generation and load demand. To address this challenge, this paper proposes a flexible tube model predictive control-based energy management regime (EMR) for prosumer CMs, enabling robustness against system uncertainties in the energy management strategy with fewer sacrifices in economic performance and computational efficiency. The proposed EMR adopts a multistage receding horizon optimization structure, which allows the prosumers to dynamically adjust their energy scheduling according to the updated energy price and forecast information. Further, a decentralized algorithm with a conditional communication strategy is developed, highlighting less communication burden and private information preservation. Case studies on a typical prosumer CM demonstrate the effectiveness of the proposed method in confronting high system uncertainties. Notably, the proposed method ensures that CMs operate with high reliability (having a maximum energy supply shortage probability of just 0.42 %), in a low-carbon and economical manner (the local accommodation rate of renewable energy generation with low costs reaches 98.83 %), even in scenarios where disturbances occur simultaneously on both the energy supply and demand sides.