Characters With White Hair Have Mutated Quirks
Right what it says on the tin. I have a theory that white hair is a sign of a quirk mutation i.e. someone with a quirk completely unrelated to the hereditary genes they should have gotten their quirk from. This is not the same as a merged quirk, where the power from the child is unique but comes from combining both of the child's hereditary genes. Those quirks can come with their own issues but they aren't completely out of left field given who the parents are.
This one is self explanatory. It's outright stated that Eri's rewind quirk is unnatural; it's where we're first introduced to the concept of mutated quirks. And her hair has always been naturally white.
It's established by the narrative that All For One and Yoichi are the first two babies born with what would be considered a quirk by modern standards. Most notably though, both are completely different from spike-like growths their mother had.
Now, because this hasn't been animated yet, it's unclear if their mother has white hair herself or just lightly colored hair but either one doesn't debunk this idea in itself. If her hair is different then both twins have a clear mutation, and if it's the same then her growths could be its own mutation. The series does explicitly mention that their mother was exhibiting a premature quirk an entire two years before quirks as we know them were discovered so clearly there was something different about her.
This one is also clearly stated as being a mutation, and it makes sense. Shoji's environment growing up was so hostile to heteromorphic quirks to such a degree that he was violently beat and chased out of his village. If his parents had similar quirks, or any kind of physical mutation for that matter, I doubt they would have survived long enough for Mezo to be born.
The Todoroki-Himura family
This one is the hardest to justify because it's not just one case, it's at least six. Geten, Rei, Touya, Fuyumi, Natsu, and Shoto all have 50% or more white hair. It's very clearly a genetic trait here.
But Rei's genetics specifically are already questionable.
It's stated by Geten that the Himura's have a history of marrying within the family. While details are minimal, if this cycle of incest has been going on for several generations at this point, it's possible that the very ice quirk Enji sought out was a mutation due to the Himura's unstable genetics. It's not a particularly odd or destructive quirk like other, confirmed, mutations, but it is surprisingly dominant and pervasive.
All four Todoroki children have some aspect of this ice quirk, suggesting that the hair color and the quirk are linked.
Touya is also one of the only people in the series born to be unsuited for his quirk. While concepts like the Quirk Doomsday Theory apply more broadly, that theory defines quirks too powerful for the body they host, not a body so genetically twisted that they inherently can't use their ability. Touya's hair also changes in hue over time in a way very unnatural to any other character in the series, as if Rei's genetics are spreading like a virus.
While marrying Enji instead of one of her cousins did diversify the genetic pool of the kids to a degree I still am willing to believe there is some significant damage to their genetic line from all of the Himura's inbreeding and the clearest sign of that is in the ice quirk.
This one is an interesting case because Tomura's hair actually changes with the appearance of "his" quirk. Keep in mind for this part that the desaturated light blue that Tomura is typically depicted with is an error on the part of the early anime staff since the only color images of Tomura at the time had blue lighting. From the start it was intended to be white. Note that he's already being drawn with white hair in the hideout raid arc.
Up to this point, everyone with a mutated quirk has been born with white hair but Tenko wasn't. His hair turned from black to white after his decay manifested. Keep in mind though, decay was not his original quirk.
While we don't know what the initial quirk was (I personally choose to believe it was float or airwalk) he was born with one naturally before All For One took it and replaced it with Decay. Decay is also a copied and modified version of Overhaul, which we know ISN'T a mutation quirk.
Essentially, All For One artificially mutated Overhaul, and the resulting quirk caused the same physical changes that natural mutations do. The quirk itself is the source of the mutation, so passing on a mutated quirk causes the same physical changes as being born with one.
Obviously both All For One (the quirk) and One For All's original form have the ability to pass quirks to others and we've seen over a dozen different people take quirks from both of these processes and not see any changes to their hair pigment.
While being given a quirk you weren't intended to hold is unnatural it's also not technically mutagenic. Giving and taking quirks is a natural process for both AFO and OFA so while the creations of these quirks were a mutation, their intended use is not.
One For All specifically stocks and absorbs the quirks from the users. It latches onto the quirks that are already there or takes up that place where a quirk would have been in the cases of All Might and Midoriya. All For One meanwhile is playing with pre-established quirks. Unless the quirk itself is carrying a mutated strain of DNA, it wouldn't affect the one being given said quirk.
There are holes in this, namely that ED6 shows Eri's mother with her hair style/texture but at the same time anime-orginal additions are difficult to weigh since we don't know if something that insignificant got author approval. It could also be a matter of all mutants have white hair but not all white haired characters are mutants. Either way I don't think this was an intended pattern by Horikoshi, just an interesting way to spin it.
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