They could interact in a very confrontational way. Michael Jackson, with his kind heart, would likely be appalled by Muzan's evil deeds. He might use his music as a weapon to try and drive Muzan away or at least make him see the error of his ways.
Well, it could be a really strange plot. Maybe it's about Michael Jackson's music having some sort of power over Muzan. For example, his music could be so powerful that it weakens Muzan's evil intentions. Since Michael Jackson was known for his positive and influential music, it might be a story of good (represented by MJ) versus evil (Muzan).
Well, one reason could be genetics. In the Naruto universe, Kushina was Naruto's mother. So in fanfiction, the author might want to emphasize this genetic connection by making Naruto look like her. It could also be for a plot device. Maybe there's a story where Naruto's resemblance to Kushina plays an important role in uncovering some long - lost family secrets or in a prophecy.
Often in fanfiction, the resemblance between Naruto and Minato can be for emotional impact. When other characters see Naruto looking like Minato, it can stir up memories and emotions related to Minato. This can create interesting character interactions, like when the older generation sees Naruto and is reminded of Minato. It also adds an extra layer to Naruto's character as he might start to understand more about his father through this physical resemblance, like how people might react to him differently because of it.
The Vermilion Bird and Liu Chuyu looked the same because they were twin sisters. The Vermillion Bird had always thought that it was a coincidence that she looked like Liu Chuyu. It was only when she accidentally overheard the conversation between the Empress Dowager and her personal maid that she found out that she and Liu Chuyu were twin sisters. The Empress Dowager abandoned the Vermilion Bird because the Celestial Master had declared that she was a jinx and could not live in this world. Therefore, for her own benefit, the Empress Dowager ordered the maidservant to kill the Vermilion Bird, but the maidservant could not bear to kill the little princess, so she abandoned her in the market. Therefore, the reason why Vermilion Bird and Liu Chuyu looked the same was because they were twin sisters.
Well, in some fanfics, the author might want to create a unique or interesting take on the character. Maybe it's for a comical effect, like having a gender - bender situation where Kirito's appearance as a girl can lead to all sorts of funny misunderstandings among the other characters in the SAO world.
Maybe it's because of its unique and charming design. Tiny houses often have creative layouts and details that seem to come from a world of imagination, like little secret hideaways.
It could be for symbolic or aesthetic purposes. Maybe they wanted to create a certain visual impact or convey a hidden message through the resemblance.