Avoiding faradaic side reactions during the operation of electrochemical devices is important to enhance the device stability, to achieve low power consumption, and to prevent the formation of reactive side‐products. This is particularly important for bioelectronic devices, which are designed to operate in biological systems. While redox‐active materials based on conducting and semiconducting polymers represent an exciting class of materials for bioelectronic devices, they are susceptible to electrochemical side‐reactions with molecular oxygen during device operation. Here, electrochemical side reactions with molecular oxygen are shown to occur during organic electrochemical transistor (OECT) operation using high‐performance, state‐of‐the‐art OECT materials. Depending on the choice of the active material, such reactions yield hydrogen peroxide (H2O2), a reactive side‐product, which may be harmful to the local biological environment and may also accelerate device degradation. A design strategy is reported for the development of redox‐active organic semiconductors based on donor–acceptor copolymers that prevents the formation of H2O2 during device operation. This study elucidates the previously overlooked side‐reactions between redox‐active conjugated polymers and molecular oxygen in electrochemical devices for bioelectronics, which is critical for the operation of electrolyte‐gated devices in application‐relevant environments.