We examine how social media users from eight European Union (EU) member states express their socio-political identities, focusing on users' online self-presentation and group identity cues conveyed through bios. Our goal is to explore commonalities and differences in topics discussed in social media profiles, across Left-and Right-wing user groups, within and across EU countries. Through a novel approach we map how identity-related discourse varies by country and political orientation, revealing how group identity is expressed within the EU. We find that topics related to democracy, national way of life, and decentralization emerge as particularly divisive, showing considerable variation both within and between EU countries. A subset of topics, which includes education, environmentalism, sustainability, equality, freedom & human rights, and traditional morality, among others, clearly differentiate Left-from Right-leaning user groups. These partisan topics are relevant as they could be leveraged for mobilizing ideological groups and highlight Left-Right identitarian differences at the EU level. Finally, we show that our Left-Right identity similarity metrics reflect aspects of real-world political fragmentation, which are closely aligned to the perceptions of political conflict intensity by country, as measured by the 2022 PEW survey.