This ticket will almost certainly NOT affect your insurance. While I cannot speak for KC, in St. Louis the red light camera tickets do not come with any points. In effect, they are nothing more than super-expensive parking tickets.
As for "getting out" of a red-light ticket, I have been able to get a couple of these waived, but only if you have a very valid reason for running it. For example, was it a very close call? Was there a semi truck in front of you that ran a yellow light, such that you didn't see that the light was red until it was too late? Was the sun rising/setting, which made the glare affect your ability to properly see the light? In St. Louis, you can challenge these tickets and you, (and your attorney, if you hire one) will actually sit with the judge and watch the video of your incident. If you think you have a valid excuse, find yourself an attorney and challenge this. Otherwise, bite the bullet, pay your fine, and be more careful next time you're at that particular intersection.