Orcs and the like are often depicted with green skin, what kind of evolutionary pressures would lead to mammals with green, blue, etc. skin and/or hair?
There is a flaw in your reasoning here. You assume that there has to be an evolutionary advantage for something to happen.
In many cases though so long as there isn't a disadvantage then something that does no harm can easily exist. For example human hair comes in a wide range of styles and colours because none of them has a significant advantage over any other so natural variance comes into play.
So long as green skin is just as effective as some other colour (or maybe it's selected for because potential mates think it looks good in which case it just has to not be too much of a drawback) then it's just natural variance.
The green Orc is rather a product of dehumanization in the creation process rather than IRL settings.
What I mean is that author think "hmm what I can do to make Orc appear not humans? I know, I give them reptile appearance so they will be perceived as cold and sleazy".
But in magic/fantasy word the circumstances would be environmental. For example: when I was a kid I've had hair that were' almost white gold. Like straw. Because kids like to run and it's harder to spot bright point in field of wheat. When I grew older my hair turn tortoise. So I have patches of colors on my head. White, black and reddish/deep red. Because adult specimen should be easy to blend when hunting for prey.
Also Orc can have certain color from their diet. Living in forest, eating roots give them green color. Living in mountains eating mountain thistle give them light blue/white color.
One reason for green skin can be skin cells' stability. As you already know, Sun's UV radiation can provoke skin cancer. This happens because high energy photons can tear away atom's outer electrons, turning them into ions with positive charge and increasing chances that regular biochemistry won't work as it should. Some molecules can be fragile to a degree, where the same effects can be produced by a mere green light. But then, if your skin contains a lot of green pigment, it means it reflects green light more than any other, thus protecting you. Blue and violet pigments will do the same job against the bands of spectrum with even greater energy.
Another reason can be this - orc's skin contains chloroplasts and is capable of photosyntesis. Such feature should have appeared in their evolutionary line long time ago, presumably before their ancestors became multicellular. Maybe it was the preferred evolutionary line because photosyntesis in their environment gave much more energy than is possible with our Sun, so many species received those legacy genes.
Yet another reason: this is mimicry. Orcs weren't always strong predators they are now (imagine goblins), so they had this adaptation to help them survive in their forests.
Or even this: it's skin sickness, similar to melanomes produced by papilloma virus. Not quite destructive for the host, but everyone out there is infected.
Another possibility is that they are green because of something they eat. Like flamingos are pink because of what they eat:
"The pink or reddish color of flamingos comes from carotenoids in their diet of animal and plant plankton. These carotenoids are broken down into pigments by liver enzymes."
There could be something other than evolutionary going on. Besides the pink flamingo getting their coloring from their foods, things can become colored because of what they are exposed to.
Sometimes referred to "smurf syndrome," argyria is a condition where a person has "excessive exposure to chemical compounds of the element silver, silver dust."
This causes their skin to turn purple, either in patches or in total.
Like the flamingo, though, eating excessive amounts of vitamin C can cause a skin color change to yellow and even orange. It's extremely temporary, as vitamin C gets flushed from your system really quickly, and it damages kidneys and other organs.
It could also be an evolutionary change to using camouflage pigments/makeup to hide in the forest, so the skin picks up the pigments after constant use and the person/orc no longer needs to reapply. This (eventually) gets transferred to their decedents generating the green/brown/black coloring naturally.