Low-carbon hydrogen is expected to play a key role in the European energy transition. The production of hydrogen using electricity in an electrolysis process is a promising route. However, depending on the origin of the electricity, hydrogen production is associated with different carbon emissions and costs. While a strict coupling of renewable energies to electrolysers ensures the ‘greenness’ of the product, it likely leads to higher production costs. On the contrary, procuring electricity freely at power markets unleashes the flexibility of electrolysers, allowing them to benefit from price signals and possibly reducing production costs. However, the carbon intensity in both the power system and the resulting hydrogen product might rise. Consequently, there is a tradeoff between environmental integrity and economic viability which affects social welfare and the decarbonisation process. By applying an electricity market model, we assess the impact of various regulatory options for the operation of electrolyser systems on social welfare and carbon emissions. These options are based on the three dimensions proposed in the ongoing regulatory discussions: (1) the origin of the sourced electricity, (2) the temporal correlation of the production of hydrogen and renewable electricity and (3) their spatial correlation. For the case of Germany in 2030, we find that the most environmentally friendly regulation reduces CO2 emissions by 4.7 Mt and the best economic outcome results in 0.9 Billion EUR of welfare gains. While too stringent regulation on the spatial dimension is not recommended, the various advantages of relatively strict requirements in the temporal dimension (e.g., decline in CO2 emissions, financial exoneration of consumers, reduction in natural gas demand) exceed their comparably moderate economic disadvantages. Moreover, we find that with a progressing energy transition, the need for such regulation diminishes, as electricity from renewable energies represents both the best economic and the best environmental option, so that the observed trade-off disappears.