The negative environmental impact of the construction sector has garnered global attention, and as the “primary force” in achieving the “double carbon” target, green development is urgent, and social responsibility practices cannot be postponed. An evolutionary game model was constructed by combining the rank-dependent expected utility (RDEU) theory and the evolutionary game theory to understand the interaction mechanism between participants’ emotions and decisions, taking into account the characteristics of construction enterprises and the public regarding irrational decisions under heterogeneous emotional combinations. The study demonstrates that: (1) there is probability in the choice of rational strategies, and emotion is an irrational factor that can affect strategy choice. (2) The evolutionary trend of the strategy choice of the game subjects is altered by emotional intensity and emotional propensity. The optimism of construction enterprises inhibits their socially responsible practice, and the pessimism of the public promotes the probability of their negative strategy choice. Furthermore, moderate optimism is a safety valve for the public’s positive strategy choice. (3) The interaction of emotional states leads to a heterogeneity of strategy choices exhibited under different combinations of emotions, with the emotions of construction companies having a more dominant influence on strategy. Finally, we make some feasible recommendations for improving social responsibility practices and preventing mass incidents by boosting emotional monitoring and guidance for construction businesses and the general public. Overall, this study provides important information about how to be socially responsible, maintain good relationships with the public, and protect the environment.