Distrust in scientific expertise is dangerous. Opposition to vaccination with a future vaccine against SARS-CoV-2, the causal agent of COVID-19, for example, could amplify outbreaks, as happened for measles in 2019. Homemade remedies and falsehoods are being shared widely on the Internet, as well as dismissals of expert advice. There is a lack of understanding about how this distrust evolves at the system level. Here we provide a map of the contention surrounding vaccines that has emerged from the global pool of around three billion Facebook users. Its core reveals a multi-sided landscape of unprecedented intricacy that involves nearly 100 million individuals partitioned into highly dynamic, interconnected clusters across cities, countries, continents and languages. Although smaller in overall size, anti-vaccination clusters manage to become highly entangled with undecided clusters in the main online network, whereas pro-vaccination clusters are more peripheral. Our theoretical framework reproduces the recent explosive growth in anti-vaccination views, and predicts that these views will dominate in a decade. Insights provided by this framework can inform new policies and approaches to interrupt this shift to negative views. Our results challenge the conventional thinking about undecided individuals in issues of contention surrounding health, shed light on other issues of contention such as climate change, and highlight the key role of network cluster dynamics in multi-species ecologies.