The fact that internet companies may record our personal data and track our online behavior for commercial or political purpose has emphasized aspects related to online privacy. This has also led to the development of search engines that promise no tracking and privacy. Search engines also have a major role in spreading low-quality health information such as that of anti-vaccine websites. This study investigates the relationship between search engines' approach to privacy and the scientific quality of the information they return. We analyzed the first 30 webpages returned searching 'vaccines autism' in English, Spanish, Italian and French. The results show that alternative search engines (Duckduckgo, Ecosia, Qwant, Swisscows and Mojeek) may return more anti-vaccine pages (10 to 53 percent) than Google.com (zero). Some localized versions of Google, however, returned more anti-vaccine webpages (up to 10 percent) than Google.com. Our study suggests that designing a search engine that is privacy savvy and avoids issues with filter bubbles that can result from user tracking is necessary but insufficient; instead, mechanisms should be developed to test search engines from the perspective of information quality (particularly for health-related webpages), before they can be deemed trustworthy providers of public health information.