Spanish healthcare workers’ professional identity is intricately associated with the idea of vocation, among others values. This attitude has become even more marked during the current COVID-19 pandemic—during which these professionals have endured a gruelling workload that has tested the limits of their physical and mental strength. The objective of this study is to open a debate on the symbolic dimensions of identity and culture among healthcare professionals (mainly doctors and nurses), analysing the factors that, on the one hand, might reinforce this symbolic system or, on the other, might question it or cause it to be restructured. The study follows an anthropological perspective, with the thematic content analysis of twenty-two in-depth interviews with primary healthcare professionals. The results show the need to dissect the symbolic and structural factors underpinning anxiety and fear in medical professional performance during the COVID-19 pandemic. These have a significant impact on the current model of medical practice and its most visible and worrying consequence, continuous occupational distress. The conclusions suggest that these models need to be reviewed since there is a notorious dissonance between their strengths and weaknesses.