Stoicism is not resigned helplessness. It is a realization that you can do what you feel you need to do (vote/protest/influence) while also realizing that the outcome is not under your control.
An important part of Stoicism is making purposeful "responses" instead of suffering kneejerk "reactions." You can be more effective in all things, including political action, if you can master this.
I will also point out that one of the founding documents is Meditations by Marcus Aurelius, a Roman emperor. He was nothing if not political.