The prevalence of hate, threats, gender trolling, and other problematic communication patterns in social media prompts concerns about the responsibility associated with government social media adoption. In addressing this issue, this paper adopts a feminist perspective to enrich our understanding of how governments assume responsibility for their adoption of social media. The study contains a sentiment and thematic analysis of responses to a government video campaign on Facebook, which seeks to heighten public awareness about men's violence against women by highlighting problems surrounding sexist jokes. The video targets two audiences in terms of gender, resulting in various outcomes in sentiments, trolling, and trolling management. Results show disparities in sentiments between males and females, the diverse strategies employed in trolling, and how both users and the local government manage trolling. The local government deploys different strategies for trolling management, encompassing both engaging and non-engaging approaches. Notably, engagement is constrained to the targeted male audience and male trollers. The primary responsibility for trolling management is delegated to users, predominantly women, who become proxies for the local government. This dual practice of ignoring women as relevant stakeholders and utilizing them as proxies is considered a failure of responsibility. The study contributes to the advancement of citizen engagement research by delving into the intricate dynamics of trolling and trolling management within the specific context of government social media. Moreover, it sheds light on issues of responsibility inherent in the adoption of social media by governmental entities.