Investigating the impacts of (non-)disruptive climate protests on social media discourses is critical for understanding their role in shaping climate policy debates. This study examines whether the attention these protests garner on Twitter leads to a juxtaposition of competing climate policy positions or instigates ideologically and affectively polarized discourses. We analyze Twitter debates around two prominent German climate movements – Fridays for Future and the Last Generation – employing automated content and network analyses (N=~5,000,000), as well as manual content analyses (N=3,000) on data compiled during 2022 and 2023. We thereby identify the types of (extreme) frames of protest events, central users, and interaction patterns integrated within the network that draw and maintain attention to the protests. The results demonstrate a consistent relationship between user networks, attitudes, and frame distribution across both debates, suggesting that all forms of climate protest stimulate online discursive tensions. These tensions facilitate the emergence of antagonist counterpublics, which criticize the protesters and their demands. The discourse surrounding the Last Generation, however, shows a significantly higher number of antagonist users, more extreme frames, less diverse network clusters, and more toxic cross-group interaction. These processes seem to be accompanied by significantly higher traffic levels, suggesting that the Last Generation's protest and communication strategies effectively draw attention to climate policy goals, albeit at the cost of increasing the counterpublics’ size and generating a more polarized debate that evenly divides users into two distinct camps. The broader implications of these findings are further discussed.