Public opinion on sociocultural issues in Europe has grown increasingly multidimensional. Preferences on gender equality and sexuality are often independent of preferences on immigration. Meanwhile, some political parties combine anti-immigration stances with moderate or progressive positions on traditional morality. This article addresses two key questions: First, are nativist voters more likely to support platforms that are also conservative on traditional morality? Second, do voters with moderate views on immigration favor anti-immigration platforms when bundled with progressive positions on traditional morality? Despite this multidimensionality, I argue that the voting space remains largely unidimensional. Two theoretical mechanisms support my argument. First, conflict on “new issues” related to gender and sexuality may be embedded in the existing sociocultural dimension. Second, issue preferences may be non-separable, meaning voters assess policy platforms as bundles rather than additively. Thus, when immigration is more important to voters than traditional morality, immigration preferences may dominate their choices. Using an original pre-registered survey experiment in Germany, along with descriptive data from Germany and the United Kingdom, I find evidence for these claims. This article highlights how the re-politicization of gender, sexuality, and gender identity issues shapes political conflict in Europe.