Peer-to-peer (P2P) energy and carbon sharing among prosumers promotes the local decarbonization, yet it faces new challenges due to the dynamic roles and heterogeneous individual characteristics of prosumers. This paper considers the social behavior and low-carbon preferences of prosumers, and proposes a novel matching-based energy and carbon sharing scheme. First, a bidirectional carbon emission obligation transfer model via sensitivity coefficients is developed, enabling dynamic allocation of emission obligation based on the energy sharing strategies of prosumers. Second, the hybrid preference model of prosumers in P2P energy and carbon sharing is formulated, which integrates, besides economic-based preferences, the considerations of social behavior and low-carbon preferences. Third, a supply-demand ratio (SDR) based proposal method combined with a modified stable matching algorithm is developed, achieving faster market clearing than conventional alternating direction method of multipliers (ADMM) methods while guaranteeing weak Pareto-optimality. Implemented on an IEEE 33-bus system with 32 prosumers, the proposed matching-based energy and carbon sharing scheme can enhance the participation of prosumers, encourage prosumers to choose cleaner energy, and then reduce the total carbon emissions of cluster.