Well, after a couple minutes of searching, I found a couple of things. In the game, Ryuji does dye his hair, but he doesn't do it for Ann. However, I do have a couple of ideas of where the concept of dyeing his hair for Ann comes up. The biggest thing I found was a YouTube video titled "Anne and Ryuji (Comic Dub) - Persona 5". In the video, it does show that Ryuji dyed his hair for Ann, but it's not canon to the game, and in the description, it says it's "An artist's interpretation of why Ryuji dyed his hair," which means that this isn't officially canon. However, in the comments, multiple people said that this was their headcanon, which means that it's the viewer's idea of what happened although it may not be official to the game. Another thing that I want to mention is the time frame. As said in a cutscene, Ryuji and Ann attended the same junior high for a couple of years and even there, she stood out. Ryuji only dyed his hair once he attended Shujin because Kawakami knew that his hair was black originally. This shows more proof that Ryuji dyeing his hair for Ann is entirely headcanon because he knew her earlier but didn't dye it until high school. In conclusion, Ryuji never dyed his hair for Ann in game, but some people find that idea so wholesome that they consider it to be true in their eyes even if it doesn't line up with what officially happened. There's nothing inherently wrong with thinking that he dyed his hair for Ann (as it gives more of a reason why he dyed his hair for a reason other than delinquency,) but keep in mind that it never canonically occurred. I hope that this cleared up some of the confusion on this topic for you.

Wait so why does he do it

that was an amazing answer thank youwu. as for renbestrickster, other then what i thought was canon, it's mainly cause he's rebellious, and from my understanding dying hair in japan is viewed as delinquency.