The emphasis on carbon emission reduction has been increasing worldwide. This paper considers a supply chain consisting of a manufacturer and a retail platform under cap-and-trade regulations. The manufacturer could invest in renewable energy to reduce carbon emissions and add a direct channel to encroach on the market. The platform could engage in low-carbon propaganda to attract environmentally conscious consumers. A two-stage Stackelberg game is built to investigate the individual, joint, and mutual effects of the manufacturer encroachment and the platform low-carbon propaganda on the supply chain. Theoretical analysis and numerical experiments show that both the manufacturer encroachment and low-carbon propaganda encourage the manufacturer to increase the renewable energy investment quantity. When the carbon trading price is relatively low, the manufacturer will encroach on the market. This encroachment, in turn, promotes the platform to engage in propaganda. Besides, the propaganda always benefits the manufacturer, who could therefore share the costs with the platform to encourage it to engage in low-carbon marketing. This not only enhances social welfare but also enables the government to subsidise the cost to stimulate the platform to propagandise. Finally, we find that the propaganda could mitigate the effects of the cap-and-trade regulation on the supply chain.