Every OTHER form of transportation...
Certainly does not stop at every red light. Specifically pedestrians. Bikes are more maneuverable and faster than pedestrians while decreasing safety only by the slightest margin if even any. I honestly don't see the problem.
Also I think it's important to note that there is no term for "safely crossing an intersection even though the light is red." That and blowing through indiscriminately are both referred to as "running" which I think contributes to a large problem in perception.