Why do linear velocity redshifts correspond to linear pixel shifts when the spectra are binned in constant log wavelength?
All this means is that you need to bin your spectra in equal intervals of log wavelength for each pixel to be a constant interval in velocity.

First consider the case whereeachpixel is worth a constant interval in linear wavelength. Here we have
$$ \frac{\Delta \lambda}{\lambda} = \frac{\Delta v}{c},$$
and the $\Delta v$ represented by each pixel depends on $\lambda$, which changes across the spectrum.

But now if you bin in equal increments of 
$$\Delta \log \lambda = \frac{\Delta \lambda}{\lambda} = \frac{\Delta v}{c}$$ 
and each pixel has the same fixed velocity interval, $\Delta v = c \Delta \log\lambda$, independent of $\lambda$.

This log wavelength binning is a prerequisite for cross-correlation procedures that yield velocities.