Many publicly debated issues have implications for health, including smoking, pesticides, food additives, seat belts, fluoridation, vaccination and climate change. Campaigners on such issues use a variety of methods, including presenting evidence and arguments, denigrating opponents, lobbying and organising protests. In some cases, campaigners seek to censor opponents, most commonly on the grounds that their views are false and dangerous. To probe rationales for censorship, recent events in the Australian public debate over vaccination are examined. A citizens' group critical of vaccination has come under heavy attack, with pro-vaccination campaigners and politicians trying to shut down the group and restrict its speech. This case study provides a window into arguments about free speech on scientific controversies with implications for public health. It highlights the tension between the alleged dangers of expressing ideas and the value of open debate in a free society.