Imagine Dean is turned into a lion, the king of the jungle. He would be more dominant and protective. Sam as a deer would seem more vulnerable, but his cleverness would still shine through. Castiel as an eagle would be aloof yet have a great vantage point. Their relationships would shift. Dean might feel more responsible for protecting Sam, and Sam might initially resent it a bit. Castiel, from his eagle's perspective, would see things differently and might have to mediate between them, all while they figure out how to turn back to their human forms and keep their friendship intact.
Well, let's say Dean becomes a horse, strong and dependable. Sam as a snake might make Dean a bit wary at first, but Sam's intelligence in his snake form would still be useful. Castiel as a sparrow would be more delicate. Their relationships would change in that they'd have to communicate in different ways. Dean's horse neighs and body language, Sam's hissing and slithering, and Castiel's chirping would all be new forms of communication. They'd have to learn to understand each other all over again, which could strengthen or test their relationships depending on how they adapt.
One idea could be that Dean turns into a wolf. He could use his new wolf instincts to hunt monsters more effectively, but also struggle with the wild side of his new form. Sam might become an owl, using his enhanced vision to spot clues from high above. Castiel could be turned into a deer, which would be ironic considering his angelic nature. He'd have to learn to be more in tune with nature.
When the TMNT turn into dragons, their relationships could shift in various ways. Their usual dynamic of being a team of mutant turtles would be disrupted. Maybe Mikey would be the most excited about their new forms and try to get his brothers to embrace the dragon - like qualities more. Raphael might struggle with the change and become more withdrawn, causing the others to reach out to him more. Their relationships would be a mix of adjusting to the new physical forms and the emotions that come with it.
His relationships with his male friends might become more complicated. Some might be more protective of him as a girl, while others might be confused about their feelings towards him. For example, if he had a rival before, that dynamic could shift completely.
Her relationships with humans would likely become strained. Humans might be afraid of her now that she's a vampire. Her romantic relationships could also change. If she had a human lover, they might have to reevaluate their relationship. And her friendships with other vampires could shift too, depending on how they view her new status as a turned vampire.
His relationships would change drastically. His work colleagues, for example, would notice his different behavior. He might start to work at night and avoid daylight. His relationships with other vampires could also be complex. He could form alliances with some vampires who are more sympathetic to his situation, while others might see him as an outsider. In his social circle, he would become a mystery to those who knew him before, and he would have to find new ways to interact with people.
His relationship with Luffy would become more of a big - brother - little - brother dynamic. Luffy would likely play with baby Zoro a lot. Sanji might be more nurturing towards baby Zoro, which is a big shift from their usual banter. Nami and Robin would probably dote on him more, and Usopp might try to come up with little games for baby Zoro.
His relationship with Tails would be strained. Tails would be confused and a bit scared at first. Sonic would have to hide his new vampiric urges from Tails, which would create distance between them. With Knuckles, there might be more of a distrust as Knuckles is very protective of their world. Knuckles might see Sonic as a threat now that he's a vampire.
With his love interests, if he had any, it would be completely different. If he was interested in a girl before, she might see him as a rival now. And if there were guys who had a crush on him as Superboy, they might be confused or even more attracted to him as a girl. Also, his relationship with his family members, like his father figure, might change as they adjust to his new gender.
In a fanfiction where Natsu turns into a girl, his relationships would be turned upside down. His relationship with his friends would be filled with awkward yet endearing moments. His male friends might have a hard time adjusting at first, but gradually they would accept the new Natsu. Natsu's relationship with the female characters would also change. He might find himself being included in more girl - only activities, which would strengthen his bonds with the female members of the guild. And his relationship with the outside world, like with other guilds or villains, would also be different. Enemies might underestimate him because he is now a girl, but Natsu would prove them wrong with his strength and determination.
If Naruto was turned into a monster in fanfiction, his relationship with the village would change drastically. The villagers who have finally started to accept him as a hero would once again be fearful. His friends would be divided in their reactions. Some, like Shikamaru, would immediately start thinking of ways to solve the problem. Naruto's relationship with his mentor, Kakashi, would be put to the test. Kakashi would have to balance his duty to the village and his loyalty to Naruto. And Naruto himself would feel isolated, which could further impact his relationships as he might become more withdrawn in his monster form.