Online mental health communities (OMHCs) are an effective and accessible channel to give and receive social support for individuals with mental and emotional issues. However, a key challenge on these platforms is finding suitable partners to interact with given that mechanisms to match users are currently underdeveloped or highly naive. In this study, we collaborated with one of the world's largest OMHCs; our contribution is to show the application of agent-based modeling for the design of online community matching algorithms. We developed an agent-based simulation framework and showcased how it can uncover trade-offs in different matching algorithms between people seeking support and volunteer counselors. We used a comprehensive data set spanning January 2020 to April 2022 to create a simulation framework based on agent-based modeling that replicates the current matching mechanisms of our research site. After validating the accuracy of this simulated replication, we used this simulation framework as a "sandbox" to test different matching algorithms based on the deferred acceptance algorithm. We compared trade-offs among these different matching algorithms based on various metrics of interest, such as chat ratings and matching success rates. Our study suggests that various tensions emerge through different algorithmic choices for these communities. For example, our simulation uncovered that increased waiting time for support seekers was an inherent consequence on these sites when intelligent matching was used to find more suitable matches. Our simulation also verified some intuitive effects, such as that the greatest number of support seeker-counselor matches occurred using a "first come, first served" protocol, whereas relatively fewer matches occurred using a "last come, first served" protocol. We also discuss practical findings regarding matching for vulnerable versus overall populations. Results by demographic group revealed disparities-underaged and gender minority groups had lower average chat ratings and higher blocking rates on the site when compared to their majority counterparts, indicating the potential benefits of algorithmically matching them. We found that some protocols, such as a "filter"-based approach that matched vulnerable support seekers only with a counselor of their same demographic, led to improvements for these groups but resulted in lower satisfaction (-12%) among the overall population. However, this trade-off between minority and majority groups was not observed when using "topic" as a matching criterion. Topic-based matching actually outperformed the filter-based protocol among underaged people and led to significant improvements over the status quo among all minority and majority groups-specifically, a 6% average chat rating improvement and a decrease in blocking incidents from 5.86% to 4.26%. Agent-based modeling can reveal significant design considerations in the OMHC context, including trade-offs in various outcome metrics and the potential benefits of algorithmic matching for marginalized communities.