In recent years, not only firms but also consumers are required to consider social responsibility (SR), particularly with regard to environmental concerns. This paper assumes that firms consider both environmental responsibility (SRE) and consumer-related social responsibility (SRC), and investigates whether consumers are attentive to SRE. As government intervention in environmental measures, the government imposes a carbon tax on firms, provides subsidies for SRE and SRC, implements rewards and penalties for the collection of used products, and introduces a cap-and-trade scheme (CTP). This paper constructs a dual-channel green closed-loop supply chain (DCGCLSC) that incorporates product sales through both offline channel (RC) and online one (OC) to expand the market reach. It proposes the optimal strategy, including the selection of the used-product collection channel, to be handled by either a manufacturer or a retailer. This paper investigates four models (N, M, R, and MR), depending on whether the manufacturer and/or the retailer engages in SRC. For each model, the optimal strategy is determined under three strategic frame works: the integrated strategy (Strategy C), the manufacturer Stackelberg game (Strategy MS), and the retailer Stackelberg game (Strategy RS). In the numerical analysis, this paper provides numerical examples and compares the optimal strategy and the social welfare for each model. The sensitivity analysis verifies how the variations in the proportion of green consumers (γ), the product value to SRC (χ) and consumers’ sensitivity to the value of used products (ξ) affect the social welfare and the selection of optimal collection channel strategy.