Developing renewable energy has become a major strategy for China to accelerate the energy transition and combat climate change. Accordingly, a guarantee mechanism for renewable energy consumption with renewable portfolio standards (RPS) has been set in China. However, currently, the top-down allocation of regional renewable energy consumption targets often has issues of unfairness and inefficiency. It is necessary to investigate the issue of how to stimulate the renewable energy consumption potential on the demand side and reasonably formulate the consumption responsibility weights of various market entities. This paper aimed to develop a new methodology for the weight allocation of renewable energy consumption responsibilities. In doing so, an integrated model of an evolutionary game and stochastic optimization was constructed between market entities and governments. Then, the equilibrium strategies of market entities and governments were obtained through the evolutionary game. Furthermore, based on the equilibrium strategies, this paper optimized the renewable energy consumption weight of each market entity, which constitutes the optimal allocation scheme of renewable energy consumption responsibility weights. Finally, using the data of 7069 market entities in Hubei Province in 2021, this study simulated the model to verify its effectiveness and practicability. The results indicate that the willingness of market entities to assume more consumption responsibility is positively correlated with the government’s incentives and the maturity of the green electricity trading market. This study provides important implications for optimizing government regulations and promoting renewable energy consumption.