During the COVID-19 pandemic, pro-vaccine and anti-vaccine groups emerged, influencing others to vaccinate or abstain and leading to polarized debates. Due to incomplete user data and the complexity of social network interactions, understanding the dynamics of these discussions is challenging. This study aims to discover and quantify the factors driving the controversy related to vaccine stances across Kuwaiti social networks. To tackle these challenges, a graph convolutional network (GCN) and feature propagation (FP) were utilized to accurately detect users’ stances despite incomplete features, achieving an accuracy of 96%. Additionally, the random walk controversy (RWC) score was employed to quantify polarization points within the social networks. Experiments were conducted using a dataset of vaccine-related retweets and discussions from X (formerly Twitter) during the Kuwait COVID-19 vaccine rollout period. The analysis revealed high polarization periods correlating with specific vaccination rates and governmental announcements. This research provides a novel approach to accurately detecting user stances in low-resource languages like the Kuwaiti dialect without the need for costly annotations, offering valuable insights to help policymakers understand public opinion and address misinformation effectively.