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.