Green hydrogen as an energy carrier is a beacon of hope to achieve climate goals because of its potential to reduce carbon emissions. Currently, the hydrogen demand cannot be met entirely with green hydrogen. Thus, non-green hydrogen cannot yet be waived. Consequently, this paper considers a two-stage hydrogen supply chain (SC) consisting of three manufacturers producing green, partially green, and non-green hydrogen and a retailer. In addition to retail and wholesale prices, the manufacturer of partially green hydrogen must determine how green its produced hydrogen should be. The players are under the influence of governmental instruments, i.e., taxes on producing non-fully green hydrogen and subsidies for the retailer for selling green hydrogen. In a manufacturer-led Stackelberg game, we observe that it is more purposeful to promote green technologies through incentives than to force them by taxes. For the partially green manufacturer, relying exclusively on green hydrogen is advantageous if its market share is high, if the additional costs for the conversion to green hydrogen are comparatively low, or if the green sensitivity of the customers is high.