Scholars, pundits, and politicians use opinion surveys to study citizen beliefs about political facts, such as the current unemployment rate, and more conspiratorial beliefs, such as whether Barack Obama was born abroad. Many studies, however, ignore acquiescence-response bias, the tendency for survey respondents to endorse any assertion made in a survey question regardless of content. With new surveys fielding questions asked in recent scholarship, we show that acquiescence bias inflates estimated incidence of conspiratorial beliefs and political misperceptions in the United States and China by up to 50%. Acquiescence bias is disproportionately prevalent among more ideological respondents, inflating correlations between political ideology such as conservatism and endorsement of conspiracies or misperception of facts. We propose and demonstrate two methods to correct for acquiescence bias.