Background: Conspiracy beliefs can be a major hindrance causing a lack of compliance with public health measures and, more in general, a government’s ability to enforce rules adopted to protect the public. During the pandemic, trust in scientists, government, and its responses to the health emergencies represented crucial questions. The study examines conspiracy beliefs, government legitimacy, and societal priorities in relationship with Covid-19 in 17 European countries: Bulgaria, Croatia, Czechia, Estonia, Finland, Greece, Hungary, Iceland, Italy, Lithuania, Netherlands, North Macedonia, Norway, Portugal, Slovakia, Slovenia, Switzerland using data from the 10th round of the European Social Survey held in 2021-2022. Results: Respondents are 33.351 aged 15 or more. Trust in scientists ranges from 54% in Slovakia and Bulgaria to over 84% in Finland and Iceland. One-fourth of respondents believe that groups of scientists manipulate evidence to deceive the public, from a high of 50% in Bulgaria and North Macedonia to a low of 20% in Italy, Switzerland, and Nordic countries. About 56% of respondents affirm that it is more important to prioritise public health when fighting a pandemic rather than economic activity, with slight differences among countries. Most respondents are satisfied with the way health services coped with the coronavirus pandemic, less in Bulgaria and Slovakia (80%). Those more prone to conspiracy, who believe in manipulation by scientists, have a lower education, older age, and lower interest in political and cultural life. Conclusions: This study paints a picture of the opinions of European citizens on government legitimacy and priorities related to the pandemic. The share of European people prone to conspiracy thinking is large, especially in Eastern Europe. This is of great concern for compliance with rules to be adopted during health emergencies.