Psychological, political, cultural, and even societal factors are entangled in the reasoning and decision-making process towards vaccination, rendering vaccine hesitancy a complex issue. Here, administering a series of surveys via a Facebook-hosted application, we study the worldviews of people that "Liked" supportive or vaccine resilient Facebook Pages. In particular, we assess differences in political viewpoints, moral values, personality traits, and general interests, finding that those sceptical about vaccination, appear to trust less the government, are less agreeable, while they are emphasising more on anti-authoritarian values. Exploring the differences in moral narratives as expressed in the linguistic descriptions of the Facebook Pages, we see that pages that defend vaccines prioritise the value of the family while the vaccine hesitancy pages are focusing on the value of freedom. Finally, creating embeddings based on the health-related likes on Facebook Pages, we explore common, latent interests of vaccine-hesitant people, showing a strong preference for natural cures. This exploratory analysis aims at exploring the potentials of a social media platform to act as a sensing tool, providing researchers and policymakers with insights drawn from the digital traces, that can help design communication campaigns that build confidence, based on the values that also appeal to the socio-moral criteria of people.