The enhancement of green animal husbandry has a significant effect on carbon emissions, carbon neutrality, and ecological development. Promoting the production transformation of polluting enterprises has caught the attention of local governments, and breeding companies are faced with either maintaining current practices or green development. This study investigated the evolution of decision-making processes between local governments and breeding companies from the perspective of evolutionary game theory, offering an evolutionarily stable strategy (ESS) for both parties, based on replicator dynamics. Within the model, the static rewards and punishments were framed by conventional environmental protection requirements, and the dynamic rewards and punishments were based on stricter environmental standards. Numerical simulation and sensitivity analyses were then performed. We found that when environmental protection policy was not considered, no ESS emerged in the replicator dynamic system. When tightening of environmental protection policy was considered, the system spirally converged to a stable equilibrium point. Hence, more demanding environmental protection requirements facilitated the development of green animal husbandry. Reasonable reward and punishment mechanisms can achieve the goal of the green development of enterprises under the premise of reducing regulatory costs. This study provides guidance for optimizing government decision-making and promoting the green development of animal husbandry.