Background: We investigated if people’s response to the official recommendations during the COVID-19 pandemic is associated with conspiracy beliefs related to COVID-19, a distrust in the sources providing information on COVID-19, and an endorsement of complementary and alternative medicine (CAM). Methods: The sample consisted of 1325 Finnish adults who filled out an online survey marketed on Facebook. Structural regression analysis was used to investigate whether: 1) conspiracy beliefs, a distrust in information sources, and endorsement of CAM predict people’s response to the non-pharmaceutical interventions (NPIs) implemented by the government during the COVID-19 pandemic, and 2) conspiracy beliefs, a distrust in information sources, and endorsement of CAM are related to people’s willingness to take a COVID-19 vaccine. Results: Individuals with more conspiracy beliefs and a lower trust in information sources were less likely to have a positive response to the NPIs. Individuals with less trust in information sources and more endorsement of CAM were more unwilling to take a COVID-19 vaccine. Distrust in information sources was the strongest and most consistent predictor in all models. Our analyses also revealed that some of the people who respond negatively to the NPIs also have a lower likelihood to take the vaccine. This association was partly related to a lower trust in information sources. Conclusions: Distrusting the establishment to provide accurate information, believing in conspiracy theories, and endorsing treatments and substances that are not part of conventional medicine, are all associated with a more negative response to the official guidelines during COVID-19. How people respond to the guidelines, however, is more strongly and consistently related to the degree of trust they feel in the information sources, than to their tendency to hold conspiracy beliefs or endorse CAM. These findings highlight the need for governments and health authorities to create communication strategies that build public trust.