District heating networks (DHNs) have significant potential to decarbonize residential heating and accelerate the energy transition. However, designing carbon-neutral DHNs requires balancing several objectives, including economic costs, social acceptance, long-term uncertainties, and grid-integration challenges from electrification. By combining modeling-to-generate-alternatives with power flow simulation techniques, we develop a decision-support method for designing carbon-neutral DHNs that are cost-effective, socially acceptable, robust to future risks, and impose minimal impacts on the electricity grid. Applying our method to a Dutch case, we find substantial diversity in how carbon-neutral DHNs can be designed. The flexibility in technology choice, sizing, and location enables accommodating different real-world needs and achieving high electrification levels without increasing grid loading. For instance, intelligently located heat pumps and thermal storage can limit grid stress even when renewable baseload heat sources and green-fuel boilers are scarce. Using our method, planners can explore diverse carbon-neutral DHN designs and identify the design that best balances stakeholders' preferences.