Measurement invariance (MI) is required for validly comparing latent constructs measured by multiple ordinal self-report items. Non-invariances may occur when disregarding (group differences in) an acquiescence response style (ARS; an agreeing tendency regardless of item content). If non-invariance results solely from neglecting ARS, one should not worry about scale inequivalences but model the ARS instead. In a simulation study, we investigated the effect of ARS on MI testing, both when including ARS as a factor in the measurement model or not. For (semi-) balanced scales, disregarding a large ARS resulted in non-invariance already at the configural level. This was resolved by including an ARS factor for all groups. For unbalanced scales, disregarding ARS did not affect MI testing, and including an ARS factor often resulted in non-convergence. Implications and recommendations for applied research are discussed.