I've shined many coyotes over the years. None have ever reacted to red light, as if it is invisible to them. I've never shined a coyote with a green light.
I have shined coons, deer, and rabbit with a green light. They do act like the can see the green light. Deer especially act like they can see their shadows cast from the light, if not the light itself, and it spooks them. Rabbits act like they can see the light directly and it usually spooks them. Coons act like they see the light or their shadows from the light, but it rarely spooks them. They just look at it a bit and go back to feeding. Coons and deer have no reaction to a red light. I cannot recall rabbits' reactions to red light.
You didn't ask, but I've also shined lots of animals with IR. IR seems to be invisible to deer, coons, rabbit, beaver, coyote, bobcat and rats. Hogs act like they can see IR if it is an exceptionally bright IR light and the hogs are within 30 yards of it. Fox also act like they can sometimes see the IR up close.