Can hair ever naturally grow in colors other than the standard ones?

The standard hair colors that grow naturally are (in various shades) black, brown, red (i.e. a copper-orange), blonde (i.e. a straw-yellow, golden-yellow or a yellow going on red or brown), grey, and white. As I understand, these colors are created by different combinations of two pigments, a black one and a red one, and by different degrees of absence of these pigments (I.E. albinism, hair going gray / white with age). Are there any exceptions to this scheme, though? Is there any rare natural way in which hair can end up growing some “rainbow color”, to put it in very simple terms?

It’s just a movie, but in the 1985 Swedish film “My Life as a Dog”, one of the main character’s friends was a boy with naturally green hair. Was this just scripted to make the character more interesting, or could something have caused this in real life (Swedes are stereotypically blonde; could there have been something either in the boy’s genes or in the environment that made his blonde hair seem or turn green)?

The black/brown one is eumelanin and the red/orange one is pheomelanin.

There apparently is no way for a human’s hair to be green, blue, or pink based on genetics or any naturally occurring condition. But there are apparently some chemicals that a person could be exposed to that might change their hair color - which would be more like an unintentional hair dye than a natural occurrence.

Even animals that do have blue, like some birds, it’s not usually from a blue pigment. Blue feathers are an optical effect, similar to the blue of the sky or blue eyes, resulting from their structure. In other words, if you grind up a bunch of blue feathers into powder, it wouldn’t be a blue powder.

I don’t think any mammal has hair fine enough to produce a similar effect.

Sometimes polar bears turn green.

This is actually do to algae from the water staining their coats. Polar bear fur is actually more transparent than white.

Possibly not under the visible spectrum but nature does keep dishing’ up surprises

As you point out, there really are only two hair colours, black and red and your apparent colour is dictated by whatever the combination is present.
I am not sure its possible to make green with these two pigments.
A very dark blue is possible, in fact the presence of a blue tint is often used to delineate the difference between black and very dark brown hair.

AFAIK that “blue tint” to jet-black hair is due to how light reflects off it. (See above, and how birds with blue feathers aren’t really “blue” but appear that way to due optics.)

Eh, lots of things, especially large organic molecules, glow under ultraviolet. That’s not particularly surprising.

Look at a glass of tonic water under a black light.

Gets even nicer when you add gin, even more so after the third glass.
FWIW, in Spain there is the saying “más raro que un perro verde”, that is: more unusual than a green dog. And then Pistaccio was born last year, but the color was probably due to “contact with a green pigment called biliverdin while in the womb” and was reportedly already fading when the article was written.

Well the individual hairs are transparent, but if that means their fur is technically transparent then snow, clouds etc are transparent.

There are blue rabbits, although some of the blue shading looks a bit shady to me.