The countryside plays a crucial role in constructing a robust socialist cultural nation, with rural public cultural facilities serving as the primary hub for public cultural activities and content. This paper utilizes each city and village in Henan Province as an example, with rural culture development serving as the primary research topic. The paper uses the influence of rural public cultural facilities as the main research index and constructs a relevant evaluation index system to assess their impact. Combine the subjective entropy value method and the objective hierarchical analysis method for the combination of weighting to judge the importance of the indicators. The TOPSIS method is employed to evaluate the complete impact, and the fuzzy set qualitative comparison method is employed to investigate the path of influence improvement. The government places greater importance on facility services and their social impact, and from 2015 to 2022, rural public cultural service facilities in Henan Province experienced a growth trend, transitioning from a risk level to a sensitive one. In addition, this paper proposes an influence strategy for rural public cultural service facilities. The consistency of the solution of the four combined paths is 0.997715, 0.97225, 0.97815, and 0.96524, all > 0.8, which illustrates that the influence factors such as resource construction, government intervention, and economic security will have a propelling effect on rural public cultural service facilities. It shows that influencing factors such as resource construction, government intervention, and economic security, all have the effect of promoting rural public cultural service facilities.