Michiru is a fake blonde, ok. But what about Sachi and Amane's hair colors? Both the VN and the anime stress that Michiru is a fake blonde.

Makina and Yumiko have natural hair colors...

But what about Amane and Sachi? I don't think there are too many natural redheads in the native japanese population of the Kyoto region (where Amane's parents are from), but I am almost sure no human is born with pink hair.

Is this just a case of "anime hair", and we are supposed to overlook these two hair colors (MST3k style), or is there something else abou these characters?

What about hair color as a recurring element(as @senshin pointed) in other shows?
In general blonde hair is thought to be foreign in Japan, Most foreign characters/exchange students usually have stereotypically bright blue eyes and blonde hair.

Young people who dye their hair blonde are generally attempts to be 'cool'/rebelious, and are often delinquents. For this reason it is somewhat meaningful that a character has dyed their hair blonde, as it is a thing that happens occasionally in Japan, whereas other colours are not so daring/meaningful. 

See Why are many anime characters blond? 

As for the more 'obscure' shades of hair, pink and other hair colours were originally introduced into anime as an easy way to distinguish characters without adding much more detail. 

I haven't watched le fruit de la grisaia, but I imagine that it's probably a result of these two occurrences. I have seen Clannad however , and I can confirm Sunohara's hair is dyed blonde as an attempt to be cool (however misguided that attempt may be :P)