In an era of globalization, cultural competence is necessary for the provision of quality healthcare. Although this topic has been well explored in non-Western cultures within Western contexts, the authors explore how Taiwanese medical students trained in Western medicine address intercultural professionalism dilemmas related to tensions between Western medicine and Taiwanese culture. A narrative interview method was employed with 64 Taiwanese medical students to collect narratives of professionalism dilemmas. Noting the prominence of culture in students' narratives, we explored this theme further using secondary analysis, identifying tensions between Western medicine and Taiwanese culture and categorizing students' intercultural professionalism dilemmas according to Friedman and Berthoin Antal's "intercultural competence" framework: involving combinations of advocacy (i.e., championing one's own culture) and inquiry (i.e., exploring one's own and others' cultures). One or more intercultural dilemmas were identified in nearly half of students' professionalism dilemma narratives. Qualitative themes included: family relations, local policy, end-of-life care, traditional medicine, gender relations and Taiwanese language. Of the 62 narratives with sufficient detail for further analysis, the majority demonstrated the "suboptimal" low advocacy/low inquiry approach (i.e., withdrawal or inaction), while very few demonstrated the "ideal" high advocacy/high inquiry approach (i.e., generating mutual understanding, so "intercultural competence"). Though nearly half of students' professionalism narratives concerned intercultural dilemmas, most narratives represented disengagement from intercultural dilemmas, highlighting a possible need for more attention on intercultural competence training in Taiwan. The advocacy/inquiry framework may help educators to address similar disconnects between Western medicine and non-Western cultures in other contexts.