Nationalistic identities often play an influential role in citizens' voting behavior and political engagement. Nationalistic ideologies tend to have firm categories and rules for what belongs to and represents the national culture. In a sample of 332 UK citizens, we tested whether strict categorization of stimuli and rules in objective cognitive tasks would be evident in strongly nationalistic individuals. Using voting behavior and attitudes from the United Kingdom's 2016 EU referendum, we found that a flexible representation of national identity and culture was linked to cognitive flexibility in the ideologically neutral Wisconsin Card Sorting Test and Remote Associates Test, and to self-reported flexibility under uncertainty. Path analysis revealed that subjective and objective cognitive inflexibility predicted heightened authoritarianism, nationalism, conservatism, and system justification, and these in turn were predictive of support for Brexit and opposition to immigration, the European Union, and free movement of labor. This model accounted for 47.6% of the variance in support for Brexit. Path analysis models were also predictive of participants' sense of personal attachment to the United Kingdom, signifying that individual differences in cognitive flexibility may contribute toward ideological thinking styles that shape both nationalistic attitudes and personal sense of nationalistic identity. These findings further suggest that emotionally neutral "cold" cognitive information processing-and not just "hot" emotional cognition-may play a key role in ideological behavior and identity.