For efficient and robust task accomplishment in multi-agent systems, an agent must be able to distinguish cooperative agents from non-cooperative agents, i.e., uncooperative and adversarial agents. Task descriptions capturing safety and collaboration can often be encoded as Control Barrier Functions (CBFs). In this work, we first develop a trust metric that each agent uses to form its own belief of how cooperative other agents are. The metric is used to adjust the rate at which the CBFs allow the system trajectories to approach the boundaries of the safe region. Then, based on the presented notion of trust, we propose a Rate-Tunable CBF framework that leads to less conservative performance compared to an identity-agnostic implementation, where cooperative and non-cooperative agents are treated similarly. Finally, in presence of non-cooperating agents, we show the application of our control algorithm to heterogeneous multi-agent system through simulations.