I'm just arguing for riding lawfully. That seems to be quite controversial, now I understand why there are so many cyclists riding dangerously. If we were to do that maths would it be personally safer to wear a helmet and run red lights or to go without a helmet and wait for the lights to turn green. Then we could ask which is safer for other road users.
Data from the Idaho stop laws indicate that it is safer treating red lights like stop signs (Stopping and then proceeding through the red light when clear).
So your answer is, it is safer to run red lights with or without a helmet.