Users of social media platforms based on recommendation systems (e.g. TikTok, X, YouTube) strategically interact with platform content to influence future recommendations. On some such platforms, users have been documented to form large-scale grassroots movements encouraging others to purposefully interact with algorithmically suppressed content in order to counteractively ``boost'' its recommendation. However, despite widespread documentation of this phenomenon, there is little theoretical work analyzing its impact on the platform or users themselves. We study a game between users and a RecSys, where users (potentially strategically) interact with the content available to them, and the RecSys -- limited by preference learning ability -- provides each user her approximately most-preferred item. We compare recommendations and social welfare when users interact with content according to their personal interests and when a collective of users intentionally interacts with an otherwise suppressed item. We provide sufficient conditions to ensure a pareto improvement in recommendations and strict increases in user social welfare under collective interaction, and provide a robust algorithm to find an effective collective strategy. Interestingly, despite the intended algorithmic protest of these movements, we show that for commonly assumed recommender utility functions, effective collective strategies also improve the utility of the RecSys. Our theoretical analysis is complemented by empirical results of effective collective interaction strategies on the GoodReads dataset and an online survey on how real-world users attempt to influence others' recommendations on RecSys platforms. Our findings examine how and when platforms' recommendation algorithms may incentivize users to collectivize and interact with content in algorithmic protest as well as what this collectivization means for the platform.