The modern global food system is an important driver of climate change. Policy measures are one potential lever for shifting consumption towards more sustainability. Public acceptance can be a major barrier for the implementation of such measures. Thus, a profound understanding of consumers is needed to facilitate policy support. In the present study, we therefore invited 453 participants from German-speaking parts of Switzerland to participate in an online survey in which we tested 15 policy measures for their consumer acceptance. Furthermore, we explored individual predictors that contribute to policy support. Our results show that there is a difference in the support of policy measures depending on the level of intrusiveness, making less intrusive measures more accepted than more intrusive measures. Support also varied depending on the targeted product category. Measures targeting dairy and meat products tended to be less accepted than measures targeting vegetables. Using a regression analysis, we identified behaviour (i.e. meat and dairy consumption) and food sustainability knowledge as an important predictor of policy support. The findings have important implications for policymakers, as they illustrate that personal involvement is a crucial factor in policy support. Taken together, our findings can help inform future food policies to increase consumer support and thereby facilitate sustainable behaviour change.