Decades after the scientific debate about the anthropogenic causes of climate change was settled, climate disinformation still challenges the scientific evidence in public discourse. Here we present a comprehensive theoretical framework of (anti)science belief formation and updating to account for the psychological factors that influence the acceptance or rejection of scientific messages. We experimentally investigated, across 12 countries (N = 6,816), the effectiveness of six inoculation strategies targeting these factors—scientific consensus, trust in scientists, transparent communication, moralization of climate action, accuracy and positive emotions—to fight real-world disinformation about climate science and mitigation actions. While exposure to disinformation had strong detrimental effects on participants’ climate change beliefs (δ = −0.16), affect towards climate mitigation action (δ = −0.33), ability to detect disinformation (δ = −0.14) and pro-environmental behaviour (δ = −0.24), we found almost no evidence for protective effects of the inoculations (all δ < 0.20). We discuss the implications of these findings and propose ways forward to fight climate disinformation.