Are you sure about that? There is blueshift and redshift as you move towards or away from light sources.
While the speed of light doesn't ever change no matter your reference frame, the frequency/wavelength indeed does.
While the speed of light doesn't ever change no matter your reference frame, the frequency/wavelength indeed does.
If you go back and see the original 46 galaxies that hubble plotted by comparing observed redshift to the distance hubble had observed you can see considerable 'scatter' in the observations. This scatter is due to the Doppler effect.
The velocity distance relationship in hubble's law isn't due to the doppler effect but a model that relates recessional velocity to the general expansion of the universe.