International survey data sets are analyzed with increasing frequency to investigate and compare attitudes toward immigration and to examine the contextual factors that shape these attitudes. However, international comparisons of abstract, psychological constructs require the measurements to be equivalent; that is, they should measure the same concept on the same measurement scale. Traditional approaches to assessing measurement equivalence quite often lead to the conclusion that measurements are cross-nationally incomparable, but they have been criticized for being overly strict. In the current study, we present an alternative Bayesian approach that assesses whether measurements are approximately (rather than exactly) equivalent. This approach allows small variations in measurement parameters across groups. Taking a multiple group confirmatory factor analysis framework as a starting point, this study applies approximate and exact equivalence tests to the anti-immigration attitudes scale that was implemented in the European Social Survey (ESS). Measurement equivalence is tested across the full set of 271,220 individuals in 35 ESS countries over six rounds. The results of the exact and the approximate approaches are quite different. Approximate scalar measurement equivalence is established in all ESS rounds, thus allowing researchers to meaningfully compare these mean scores and their relationships with other theoretical constructs of interest. The exact approach, however, eventually proves to be overly strict and leads to the conclusion that measurements are incomparable for a large number of countries and time points.