The rural social pension replacement rate reflects the level of social pension protection for individuals by the rural social pension insurance pillar, and is a relative indicator capable of measuring the level of pension protection by inter-period comparison under different levels of economic development. Aiming at enhancing the sustainable development strategy of rural cultural pension system, this paper establishes a sustainable development index system, uses Random Forest, Logistic Regression and Bayes as the base classifiers, proposes an integrated learning model based on the Stacking integration strategy, and Support Vector Machines as the metaclassifiers for parameter optimization, to assess the sustainable development of the pension system. Secondly, SHAP is introduced to explain the influencing factors of pension system sustainability found by the model. According to the empirical analysis and visualization analysis, the Stacking integration method is better than other single learner models in terms of accuracy, checking rate, AUC value, etc., except for the true instance rate which is lower than random forest, with values of 0.953, 0.877, 0.972, 0.949, respectively, indicating that Stacking integration can be better applied to the pension system sustainability in the assessment. Integrating the influencing factors, it is found that the development speed of the system, the economic affordability at all levels, the reasonableness of the institutional setup, and the efficiency of the management service are the main influencing factors for the sustainable development of the pension system. Finally, recommendations are made to optimize the demographic structure, improve the quality of the population, and active aging in order to cope with the risk of population aging and unsustainability of rural pensions.