Mammals don't come in green. We have 2 colours available to us, in different amounts: eumelanin, which is dark brown to black, and pheomelanin, which is yellow/red. We can mix those up in any way, or none (for white), but it'll never be green.

Now, many other animals don't have green either, peacock feathers for example, have brown pigment, but they have a structure that makes it look green and blue from wave interference.

Unfortunately, you can't really do that with fur, since you need to look at fur from all directions, not just the front.

So, mammals don't get green fur.

Evolution is throwing things against the wall and seeing what sticks (by sticking I mean reproducing bc you have better traits). If every single one of their prey and predators have this color blindness then orange and green would have the same effectiveness and whichever trait comes out first. If a prey/predator evolved to have better color vision then it would quickly become a disadvantage and after millions of years it's possible they evolve to have green fur.

There could be other benefits like being easier to attract mates.

Also some animals can see infrared, so even if their fur was perfect for the environment they could still have issues by being spotted, in which case the color doesn't matter as much and the colors for mating becomes more important.

Edit: Wording.

A) Evolution is not directed. If a pre-tiger happens to be a more advantageous colour, it will have more offspring. There is no goal.

B) An orange tiger has the same camouflage from its prey's point of view as a green one, which is the thing that really matters. There is only one species a tiger is afraid of, and it's humans. I would wager that the orange also happens to act as a signal colour, both to other tigers and other predators (such as humans). Less run-ins and less territorial dispute sound pretty good.

I don't know any animal with green fur. Reptiles and birds, sure. Maybe green fur does not work 🤷