No, light is not different. If you want to adjust for "red/blue shift", you may use special relativity, and in special relativity you have the conservation of 4-momentum, which will give you the same result.
Ah, if my understanding is correct then this makes sense.
In my initial argument I bring in relativity and the invariant speed of light. What I neglected is everything else in relativity, like lorentz transformations.
I mentioned a discontinuity between invariant speed of light and summing velocities to calculate momentum. The discontinuity is distance. Velocity is distance x time, but under lorentz transformations distance is relative. The discontinuity is resolved if you include length contraction (and time dilation).
