If we see farther away galaxies moving away at the same speed as nearby galaxies that means that all the expansion of the universe happens between us and the nearby galaxies (since the farther away galaxies wouldn't be moving away from the nearby galaxies). So we would have some kind of local expansion of space around our galaxy. This is if we see a redshift in all directions, if we see a redshift in one direction and a blueshift in the opposite direction, that just means that our galaxy is moving relative to the observed galaxies (also, such a dipole can be seen in the microwave background).