Limiting the global mean temperature increase to 1.5°C requires phasing out fossil fuel combustion almost entirely within the next three decades and replacing carbon-intensive technologies with low-carbon alternatives. Such socio-technical transitions are politically feasible only if public acceptance is sufficiently high. Here we investigate German citizens' views on the phase-out of internal combustion engine vehicles (ICEVs) using a random forest (decision trees) classification and logistic regression model. We surveyed a demographically representative sample (N = 1,663) in 2021, finding that the majority of respondents (67%) approve of an ICEV phase-out by 2040 or hold a neutral stance. Acceptability is best predicted by the degree to which environmental problems are attributed to ICEVs, followed by respondents' willingness to abandon cars altogether or adopt electric vehicles (EVs). Our results further indicate that acceptability can be increased by providing people with information that present EVs in a more favourable, and ICEVs in a less favourable light. When the European Commission proposed to ban the sale of ICEVs by 2035, we conducted a follow-up survey to investigate whether this had influenced acceptability in Germany – with the result that it had not. In terms of concrete policies, pull measures such as public transport or electric vehicle purchase subsidies are preferred by the public over more restrictive policies such as taxes or bans. The findings of this study shed light on different dimensions of public opinion and their important implications for policymaking and the political feasibility of this socio-technical transition. Insights from this research can help policymakers in designing effective yet widely acceptable transport decarbonization policies. Overall, 45% of respondents approve of an ICEV phase-out by 2040, while 34% disapprove. Acceptability is best predicted by the degree to which environmental problems are attributed to ICEVs, as well as respondents' willingness to adopt electric vehicles or give up their cars altogether. Emphasizing the advantages of electric vehicles or the adverse effects of ICEVs increases acceptability, while indicating the inevitability of an eventual phase-out does not. On average, public transport and electric vehicle purchase subsidies enjoy higher levels of public support than taxes or different permutations of ICEV bans. [ABSTRACT FROM AUTHOR]