So, while he accelerates toward it until near the speed of light in his original frame of reference, he will detect the oncoming photon as gamma radiation, but in my frame of reference where I’m not accelerating and just idling, and looking at the same photon, I’ll still see the photon as not gamma radiation at all?
Yes (if you change the wording to “if I accelerate toward it until I’m moving near the speed of light relative to my original reference frame”).
So, while he accelerates toward it until near the speed of light in his original frame of reference, he will detect the oncoming photon as gamma radiation, but in my frame of reference where I’m not accelerating and just idling, and looking at the same photon, I’ll still see the photon as not gamma radiation at all?
I think if there’s a guy accelerating to the speed of light and you’re staring at a photon, you’re missing out on some incredible things in this life.
A blueshift or redshift depends on your frame of reference. Unless you are also moving you would see a redshift or blueshift.