Social networks such as Twitter can promote social alarm about conflicts concerning anti-hate speech legislation. The protests after the prison sentences of the rappers Valtònyc (2018) and Hasél (2021) are two paradigmatic cases in Spain. This research analyses how citizens’ desire to combat hate speech may be frustrated when the law is applied. Using a quantitative and qualitative methodology, we observe the users and the media reactions on Twitter in both cases. In the first phase, we conducted a content analysis (n = 694) to identify the position of users and the media. In a second phase, discourse analysis examined the presence or absence of the features of constructive journalism in the news coverage. The results show that the anti-law stance is predominant in Twitter messages, but there are few references to freedom of expression and censorship. While there is a considerable presence of an angry style of communication and polarised messages in users’tweets, the media adopt a rational and informative approach. The media discourse in both cases is still far from the traits of constructive journalism.Therefore, this research shows that informative actions based on the principles of constructive journalism could mediate between citizen sensibility and legislation. This could promote a sense of citizenship that avoids hate speech