Renewable liquid fuels produced from biomass, hydrogen, and carbon dioxide play an important role in reaching climate neutrality in the transportation sector. For large-scale deployment, production facilities and corresponding logistics have to be established. However, the implementation of such a large-scale renewable fuel production network requires acceptance by citizens. To gain insights into the structure of efficient and socially accepted renewable fuel production networks, we propose a bi-objective mixed-integer programming model. In addition to an economic objective function, we consider social acceptance as a second objective function. We use results from a conjoint analysis study on the acceptance and preference of renewable fuel production networks, considering the regional topography, facility size, production pathway, and raw material transportation to model social acceptance. We find significant trade-offs between the economic and social acceptance objective. The most favorable solution from a social acceptance perspective is almost twice as expensive as the most efficient economical solution. However, it is possible to strongly increase acceptance at a moderate expense by carefully selecting sites with preferred regional topography.