You may have not actually run a red light. In the US, there are permissive yellow and restrictive yellow states. Some states make it illegal to pass the stop line once the light has turned red while others make it illegal to be in the intersection at all once it has.

It is good to be defensive, but try not to worry so much about others that you would place yourself in harm's way because of their unsafe driving. If you were to run a red light because someone is tailgating you, it is likely you would be held at fault for any collision that occurred as a result or even ticketed for doing so. Getting rear-ended sucks, but a crash in the middle of a busy intersection could suck even more; not to mention that you could be held responsible for the crash in the intersection while the other driver would likely be held responsible for rear-ending you.

There may come a time where you can choose to break the law to prevent a collision, but just understand that anything that happens a result of you breaking the law may fall on you. If it were me, I would brake as slowly as possible and stop before running a red light. It shouldn't be like I am rear-ended while stopped and the other person is going 40 MPH. Hopefully they would slow down safely and avoid a collision.