@Riot Why is Quinn's hair Blue or Purple

It's her natural hair colour. As in, it's actually blue/purple.

It can also be a depiction thing, such as what is commonly done in anime these days, where many characters sport brown or blue-ish hair colour when in reality they are all meant to be a figurative alternative to black hair for the purposes of visual diversity (if not also used as an indication of character/personality, which is another popular depiction method).

But given it's high fantasy setting here in League, one can not exclude the possibility that it is really just a natural hair colour people can possess in that world (there are also other blue hair and other 'odd' colours of hair in League). And honestly, I'll be more willing to bet that this is the case.

I think Riot decided to go with this hair color, because its the same as Valors feathers. And blue hair is nothing new in lol, Sona and Jinx both have blue hair aswell.

Well it does actually look like hair dye exists in runeterra,as it was once mentioned that s hair doesn't have its natural color(though the same goes for her eyes) and several other piltover/zaun champs have unnatural looking hair colors ,so it wouldn't surprise me if at least thesed factions had access to hair dyes.

Demacia might have that too,otherwise s hair wouldn't make much sense. But maybe there are just people who are born with weird hair colors,so who knows?