While Republican states have been criticized for their limited efforts to contain the spread of COVID-19, it is important to consider that political orientation can modify human behaviour via complex effects that are still poorly understood. During the first period of the pandemic, we found that the association of republicanism with US citizens' mobility varied depending on the nature of the exposure being considered. First, republicanism was associated with increased mobility when the stringency of anti-COVID measures increased. Second, republicanism was associated with decreased mobility when COVID-related deaths increased. Third, republicanism was associated with increased mobility over time, i.e. as time went by, citizens living in Republican states were more mobile than those in Democratic states. These findings raise caution on any over-interpretation of the impact of polarization in US politics on COVID-related behaviour. They prompt consideration of persuasive tools that emphasize risk perception to promote social distancing in Republican states, rather than relying heavily on stringent anti-COVID interventions.