Science museum landscapes are shifting with the emergence of controversial exhibitions. The complex nature of controversy poses interesting questions and challenges to museum staff and visitors. Our qualitative study focuses on a subset of the potential public audience for controversial exhibitions, who we call non-visitors. Through an interpretivist approach involving interviews with 13 non-visitors, we set out to understand why people deliberately chose not to attend the controversial exhibits "Body Worlds and the Story of the Heart" and "Animal Inside Out." Our findings suggest that non-visitors experienced "cultural, educational, visceral and emotional", and "ethical" constraints that affected their choices not to attend. These constraints suggest a form of controversy that is "external to science" and that invites us to critically examine (1) ethical messages privileged in the exhibits, (2) socio-cultural groups that may be alienated through exhibition choices, (3) consultation practices with diverse members of the community, and (4) scaffolding of the visitor experience.