Yes.
First, red shifting can be caused by any relative motion, not just relative motion due to the expansion of space. Things that are moving towards us - for whatever reason - will emit light that is blue shifted when it reaches us; things that are moving away emit light that ends up red shifted. It turns out that, outside our own galaxy, the vast majority of things we can see have red shifts, because the large-scale expansion of the universe has the largest effect on their relative motion. There are a few galaxies in our local group that show blue shifts, but the number can be counted on one hand, practically.
Second, light propagating through matter can pick up a red tint, because smaller wavelengths (e.g. blue or green light) tend to be scattered more than red. For example, light from a distant star that has to pass through interstellar gas clouds to reach us, often ends up looking redder than when it was emitted, because the blue and green components of the light don't reach us on Earth (or, at least, not as much, relative to red).
This second reason is why the new James Webb Space Telescope is designed to use infrared light, which is scattered and absorbed by even less than visible red light by gas and dust. That means that the JWST can see things that were invisible to Hubble (which worked in visible light).