To effectively reduce carbon emissions from the manufacturing industry and promote green and sustainable developments evolutionary game theory is widely used. This study has constructed a four-party evolutionary game model, in which the government, civil environmental protection organisations, manufacturing enterprises, and consumers participate. A local robustness analysis and numerical simulation were used to assess the stability conditions under which the strategic behaviour of the four parties reaches an ideal state, and the influence of government parameter changes on the game system were further analysed. The results show that when the government's penalty is greater, the decision-making time of civil environmental protection organisations and manufacturing enterprises is shortened to varying degrees. When the subsidy coefficient provided by the government increases, civil environmental protection organisations, manufacturing enterprises, and consumers can reduce the time required for the system to stabilise to varying degrees. As the subsidy coefficient increases, the government's strategic choice evolves and strict regulations are loosened. The government should thus actively establish a reward and penalty mechanism, according to its own actual situation, set reasonable punishment and subsidy coefficients, and actively guide the subjective initiative of civil environmental protection organisations to reduce carbon emissions in the manufacturing industry.