> if cyclists blasted through red lights without looking we would all get hit by cars within a few intersections
It is left up to the drivers and pedestrians to get out of the bicyclists' way and avoid collisions.
> of course cars have come close to hitting you
Not in my personal experience. One example is what happens when there is a red light and I have the cross signal. If I see only cars I will begin crossing, because the cars typically have already started to slow down well before the light so I know they will stop. If I see a bike I will typically wait for it to pass. And sure enough, most of the time the bike will continue through the red light.
Another example is when the light is green, and there is traffic taking a left turn into a crosswalk which has the cross signal. Cars go so slow to the point that they stop several times before completing the turn. Bikes just make the turn at full or maybe half speed, and sometimes ring their bell. Scenarios like this are what have caused most of my near-collisions. There's no chance of seeing them coming.
> It is always jarring to hear what I anecdotally believe to be a minority of pedestrians who actually believe that cyclists are in any way, shape, or form more of a threat to their safety than motor vehicles.
It does seem that both sides of this issue believe the other side is living in a bubble. All I can say is what I see. Look around any intersection in NYC where there are red lights and stopped cars. If there are any bicyclists around, they will be the fastest moving objects you can see.
From what you wrote it sounds like you've heard this more than once. So have I!