Tokyo Ghoul and Tokyo Ghoul:re follow the life of Ken Kaneki/Haise Sasaki as he is transformed into a ghoul in a freak surgical operation and construction accident. One puzzling aspect of the series is why Kaneiki's hair changes color over the course of the two series and why the author puts such effort into this detail.
There are two reasons why Kaneki's/Sasaki's hair changes color throughout the series. The first reason is direct and explicitly stated, while the other has metaphorical reasoning behind it, requiring the audience to pick up the pieces laid before them.
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Ghouls are an exclusively carnivorous and cannibalistic human species that can only feed off of either human or ghoul flesh. Feeding on humans is required once a month as going without it causes severe mental deterioration. A ghoul that goes into extreme starvation eventually loses cognition of everything around them, only seeing the rest of the world as a potential meal. In the case of Rize Kamishiro, being starved by Dr. Kano resulted in her mind being reverted to that of an animal. Consuming only ghouls manages to stave off the hunger temporarily; however, mental deterioration is inevitable.
As seen with Kaneki in the latter half of the Tokyo Ghoul manga, consuming only ghouls caused him to think more erratically, use his kagune less cautiously and isolate himself from his friends at Anteiku. Ghouls have an abnormally high amount of "RC cells" that they acquire from eating humans and ghouls and then store in a special ghoul-exclusive organ called the "kakuho." Ghouls are able to freely manipulate the density and flexibility of RC cells, allowing them to release the cells from their skin and use them as weapons or limbs. This release of RC cells from the body is called a kagune, of which there are four subdivisions: Ukaku, Rinkaku, Bikaku and Kokaku. Failing to eat human flesh results in a lack of available RC cells, making the user's kagune weaker.
Besides consuming human and ghoul flesh, there is another way to strengthen the kagune and bolster RC production. To do this, one must experience a plethora of physical pain. Similar to the Sharingan from Naruto, the more pain one endures, the stronger they become. Whether it be from torture or brutal exercise, the damage one receives strengthens the kakuho by increasing the number of cellular tubes that allow for RC cells to be released. This, in turn, creates a positive feedback loop. By enduring pain, the kakuho becomes stronger and a ghoul is able to endure more pain. This positive feedback loop serves to make a ghoul stronger in the long term.
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Kaneki was permanently traumatized by many people in his life, but they're all insignificant when compared to the impact Yakumo Oomori, nicknamed "Yamori," had on him. In a game to "break the One-Eyed," Yamori set about to permanently traumatize Kaneki by torturing him the same way Yamori was once tortured by the CCG. Kaneki is forced to count backward from 1,000 in intervals of seven to keep Kaneki sane and prevent disassociation while the torture progresses. Taking advantage of Kaneki's remarkable healing capabilities, Yamori would clip each one of Kaneki's digits off with metal pliers. He also would routinely cut off Kaneki's arms and legs to watch them grow back like fingernails. When Yamori had to leave, he would place a red-headed Chinese centipede into Kaneki's ear to tunnel around and cause him incomparable anguish.
An important result of Yamori's torture is the unintended consequence of strengthening Kaneki. By repeatedly cutting off and breaking Kaneki's limbs, Yamori had inadvertently strengthened Kaneki's kagune to far surpass his own. The torture resulted in Kaneki's hair changing from black to white because of the increase in cellular tubes in his RC cells in his kakuho, thus increasing his own RC cell count.
However, there also remains the metaphorical reason that Kaneki's hair changes color: the loss of his purity. Whenever Kaneki's innocence is irreparably damaged, his RC count spikes and his hair turns white, as seen on two occasions in both the original series and Tokyo Ghoul:re. The foremost example of this is shown when Yamori tortured Kaneki for multiple days, as his hair color is seen to change from panel to panel in Tokyo Ghoul, Chapter 61, "Glimmer." He walked into Yamori's torture chamber with dark black hair, and his hair soon lost all pigment during the torture. Following Yamori's torture, Kaneki became a completely different person desperate to protect everyone around him. His hair color denoting his innocence is reinforced in the first chapter of Tokyo Ghoul:re.
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Utilizing the "tabula rasa" trope, in Tokyo Ghoul:re, Kaneki's mind was wiped clean, and he began a new identity as Haise Sasaki working at the CCG. The most notable physical difference in Sasaki's appearance is that his hair is primarily black while the tips remain white. This alone tells the audience that Sasaki's initial RC count is significantly lower than when his identity was Kaneki. The literal answer as to why his hair regained its complexion is because Sasaki was required by the CCG to take RC suppressants.
As the name implies, RC suppressants suppress the RC cells that ghouls can access, thus impairing their kagune, regenerative abilities and thick skin. An unintentional side effect of RC suppressants is that it also temporarily increases melanin production in the hair, thereby giving back Sasaki his dark hair. As Sasaki slowly comes to terms with his former identity as Kaneki, he is also given the leeway of not having to take as many RC suppressants. Thus, as the series progresses, his hair slowly loses its color once again.
The metaphorical answer of "a reflection of innocence" for why Kaneki's hair changes color also applies in Tokyo Ghoul:re. When Sasaki has no memory of his former life as Kaneki and his innocence is at its height during the beginning of Tokyo Ghoul:re, his hair is almost black, with small patches of white at the tips. Sasaki's hair is a clear metaphor for his innocence, with the darkness of Kaneki being locked away in the corners of his mind and manifesting as white tips in his hair.
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During Sasaki's lowest point following the Tsukiyama Family Extermination Operation, his personality becomes cold and compassionless. In an attempt to protect himself from being hurt, he isolates himself from the rest of the Q squad and temporarily regains his innocence. This is proven by his hair turning completely black following the Tsukiyama Family Extermination Operation.
During the Rishima Landing Operation, Sasaki is informed by Eto Yoshimura that the CCG has a darker history than it lets on and has ghouls running the organization. Sasaki rallies his resolve and then releases all the ghouls in Cochlea ranking S and below in the incipience of what would become known as the Second Cochlea Raid. During the Second Cochlea Raid, Sasaki's hair once again adopts a uniform white complexion, indicating his repeated loss of innocence.
