One of the cornerstones of progressive "identity politics" is the notion that the struggles of disadvantaged groups are interconnected, which links together support for different group-based issues. A downstream consequence of this linkage is that support for non-contentious issues can become linked to contentious issues. In this project, we examine the consequences of such linkages by focusing on how public support for sexual minority rights (a popular, non-contentious issue) became linked to the Israel/Palestine conflict (a contentious issue) in connection with the 2024 Copenhagen Pride Festival. We hypothesize that linking these issues will decrease support for the rights of sexual minorities, and that this decreased support might extend to rights of gender minorities (a related, but less widely supported issue), and support for climate change mitigation (a widely supported, but ideologically adjacent issue). We test our hypoteses in a pre-registered survey based-priming experiment conducted in Denmark, where we randomly assign participants to conditions either implicitly or explicitly linking Pride to the Israel/Palestine conflict, or to a control conditions with no linkage. Our findings have important implications for our understanding of identity politics, issue linkages, and issue advocacy.