Instability in supply and demand, coupled with conflicting market interests, significantly impacts the operational efficiency, reliability, cost-effectiveness, and environmental sustainability of integrated energy systems. To address this issue, an operation strategy for a community integrated energy system based on Stackelberg game theory is proposed, taking into account the characteristics of supply and load. Initially, a master–slave game model for an integrated energy system is established, with energy marketer acting as leader and energy supplier and load aggregator as followers. To manage the uncertainties of wind and photovoltaic power generation, robust optimization theory is employed to construct models for both the short-term and long-term output errors of wind and photovoltaic power generation. This approach allows for a more detailed analysis of the uncertainty associated with wind and photovoltaic power generation. Subsequently, the uniqueness of the equilibrium in the established Stackelberg game model is proven. Utilizing an improved adaptive differential evolutionary algorithm in conjunction with the CPLEX solver, not only is the optimal solution solved for, but also the efficiency of the solution scheme is significantly enhanced. The simulation results demonstrate that the strategy not only boosts the reliability of the integrated energy system but also achieves a cost saving of 1.11%, an increase in energy supplier profit of 5.16%, and a load aggregator consumer surplus of 19.68%. In scenarios considering errors in wind and photovoltaic predictions, the cost savings reach 16.95%, with energy seller and supplier profits improving by 9.34% and 32.47% respectively, and consumer surplus increasing by 18.81%.