The most common explanation for the current surge of Vaccine Hesitancy is that the Internet helps vaccine science deniers reach a wide audience. This explanation is challenged by the growing success of critics who present themselves as different from antivaccinationists, using phrases such as “I’m not antivaccine but. . . ” and promoting so-called “alternative vaccination schedules”. This could mean that antivaccinationists strive to appear more moderate than they are. But it could also mean that vaccines are being taken on by less radical activists. We compare these two explanations using the contents of a large sample of French-speaking websites.add{We qualitatively coded the contents of these websites, analysed their citation patterns and assessed their presence in mainstream media.} We found that this milieu is fragmented. The most prominent activists only criticise some vaccines and disassociate themselves from the tightly-knit community of radical antivaccinationists. We also found that some appear as moderate while being deeply embedded in the community of radicals, indicating that their “moderate” stance is a communication strategy. These results suggest both explanations are simultaneously true. They apply to different activists, highlighting the importance of exploring the diversity of contemporary vaccine criticism to understand vaccine hesitancy.