Cognitive coping strategies to deal with anxiety-provoking events have an impact on mental and physical health. Dispositional vigilance is characterized by an increased analysis of the threatening environment, whereas cognitive avoidance comprises strategies to inhibit threat processing. To date, functional neuroimaging studies on the neural underpinnings of these coping styles are scarce and have revealed discrepant findings. In the present study, we examined automatic brain responsiveness as a function of coping styles using functional magnetic resonance imaging. We administered a perceptual load paradigm with contemptuous and fearful faces as distractor stimuli in a sample of N = 43 healthy participants. The Mainz Coping Inventory was used to assess cognitive avoidance and vigilance. An association of cognitive avoidance with reduced contempt and fear processing under high perceptual load was observed in a widespread network including the amygdala, thalamus, cingulate gyrus, insula, and frontal, parietal, temporal, and occipital areas. Our findings indicate that the dispositional tendency to divert one's attention away from distressing stimuli is a valuable predictor of diminished automatic neural responses to threat in several cortical and subcortical areas. A reduced processing in brain regions involved in emotion perception and attention might indicate a potential threat resilience associated with cognitive avoidance.