The increased access to online information provided by social media platforms allows individuals to form and convey their beliefs regarding events in their daily lives. The wide range of interactions carried out in these virtual environments has the power to impact the decisions and behaviours of others, also creating conflict, polarisation, misinformation, and toxic content. When individuals engage in public debates about topics tied to significant societal concerns, these discussions often regard or imply moral values. By analyzing five years of Italian Twitter/X debate on immigration, we show how a language model aware of moral values detects community structures more accurately, better depicting the actual political scenario in Italy.