Demand response (DR) is recognized as an efficient method for reducing operational uncertainties and promoting the efficient incorporation of renewable energy sources. However, since the effectiveness of DR is greatly influenced by consumer behavior, it is crucial to determine the degree to which DR programs can offer adaptable capability and facilitate the use of renewable energy resources. To address this challenge, the present paper proposes a methodological framework that characterizes the uncertainties in DR modeling. First, the demand-side activities within DR are segmented into distinct modules, encompassing load utilization, contract selection, and actual performance, to enable a multifaceted analysis of the impacts of physical and human variables across various time scales. On this basis, a variety of data-driven methods such as regret matching mechanism is introduced to establish the analysis model to evaluate the impact of various factors on DR applicability. Finally, a multi-attribute evaluation framework is proposed, and the effects of implementing DR on the economic viability and environmental sustainability of distribution systems is examined. The proposed framework is demonstrated on an authentic regional distribution system. The simulation results show that compared to scenarios without considering uncertainty, the proposed method can fully consider the impact of DR uncertainty, thereby enabling a more realistic assessment of the benefits associated with DR in enhancing renewable energy accommodation for smart distribution grids. From the comparative analysis of new energy installation scenarios, with the integration of photovoltaic and wind power into the system, the presence of DR can increase the renewable energy consumption rate by 6.39% and 37.44%, respectively, and reduce the system operating cost by 1.37% and 3.32%. Through the comparative analysis of different load types, when DR is a shiftable load and a two-way interactive load, the renewable energy consumption rate increases by 20.57% and 26.35%, and the system operating cost decreases by 2.12% and 4.68%. In this regard, the proposed methodology, hopefully, could provide a reliable tool for utility companies or government regulatory agencies to improve power sector efficiency based on a refined evaluation of the potential for demand-side flexibility in future power grids incorporating renewable energies.