In the wake of rising energy prices and the cost of living crisis, some have claimed that climate policies are at odds with citizens' more pressing everyday living concerns. Critics challenge these simplifying narratives that shorter term economic and social wellbeing priorities and ‘longer term’ decarbonization policies are in tension with one another and argue that effective policies must treat them as interconnected. Evidence regarding how citizens think about climate policy mostly focus on policy acceptability, highlighting the role of perceptions of effectiveness and fairness, but there is a quite limited conceptualization of contexts of social inequality, and even more limited engagement with the views of marginalized groups whose buy‐in is seen as crucial for effective net zero transitions. This paper reviews the evidence and analyses new data from a small exploratory study with citizens from low income and marginalized backgrounds. In group discussions several participants emphasized the importance of tackling both social hardships and climate priorities, seen by some as interlinked. Further, many described wider societal unfairness relating to experiences of poverty, exploitation, a lack of voice or even recognition and a keen sense of disconnect between politics and their own everyday concerns and lived experiences. I argue that climate policy making should engage more fully with contexts of social inequality and that social wellbeing and systematic action on climate change need to be treated by policy makers and politicians as profoundly interlinked challenges.