By increasing the amount of red light That is very different than the frequency shift seen in red shifts.
For example, if you compare *two* spectral lines from the same element, when red shifted, both lines will appear but at a lower frequency. In reddening, the lines will extinguish and be replaced by a more thermalized emission in the infrared. The effects are very different.
Galactic red shifts are not do to reddening as from interaction with dust, but are proportional changes in frequency among all points of the original spectrum.