Distrust in science has been linked to scepticism over vaccines and climate change. Using data from nationally representative surveys administered in eight key countries for global efforts to mitigate climate change and COVID-19 (Australia, Brazil, China, India, Japan, South Africa, the UK and US), we find that distrust in scientists was an important predictor variable for most sceptics, who were sceptical of one issue but not both, in February 2021, when most countries had experienced their first wave of the pandemic. However, the association was significantly weaker among the segment of hardcore sceptics who were both climate sceptics and antivaxxers. We demonstrate that these individuals tended to possess many of the typical sceptic characteristics such as high distrust in social institutions and rightward political orientation, which are (collectively) suggestive of an underlying sceptic mindset rather than a specific distrust of scientists. Our results suggest that different types of sceptics necessitate different strategies to dispel scepticism.