Naruto would be devastated. He has always idolized his father, so being betrayed by him would shatter his world. At first, he might be in denial, not wanting to believe that Minato could do such a thing.
Well, Minato being the calm and collected type, would probably approach reading Naruto fanfiction with an open mind. He might find some of the stories that depict his heroics in new and interesting ways quite fascinating. Kushina, on the other hand, would be more vocal. She'd either love the fanfiction that shows her as a loving mother and strong kunoichi or be a bit critical if it doesn't match her self - image. For example, if a fanfiction portrays her as too weak, she'd be likely to scoff at it. But overall, they'd both enjoy seeing the different ways the fans have imagined their lives.
Well, Minato might be proud to see how his son Naruto has been portrayed in the Naruto Shippuden fanfiction. He could also be impressed by the creativity of the fans in coming up with new storylines. Kakashi would likely enjoy reading different takes on his own character and the battles he's been in. Rin would probably be excited to see how her character has been explored in different ways, whether it's her relationship with Kakashi or her role in the overall story. Obito might have mixed feelings. He might be angry if the fanfiction misrepresents his motives, but also intrigued if it offers a new perspective on his journey.
Minato and Kushina's reactions could vary widely. Minato, being a strategic thinker, might initially be skeptical about how well the two very different universes of Naruto and RWBY can be combined in fanfiction. But as he reads on, he might appreciate the creativity involved. Kushina, with her fiery personality, could be excited or even a bit outraged if the fanfiction takes too many liberties with the Naruto characters she loves. She may also find it interesting to see new adventures for Naruto and his friends in this RWBY - inspired setting.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
Kushina could be an important character even though she's dead in the original story. In this fanfic, her spirit or memories could play a role in Naruto's upbringing. For example, Minato could tell Naruto stories about Kushina's feisty personality and her love for the village.
In some fanfictions, Minato saves Naruto physically. For example, he might use his teleportation jutsu to appear right in the middle of a fight and whisk Naruto away from danger. In others, he could save Naruto spiritually. He might enter Naruto's mind, like in the fanfic 'Minato's Mind - Saving Mission', and give him the strength and confidence to overcome his inner demons. Sometimes, Minato saves Naruto from a political situation. For instance, in 'Minato and the Hidden Leaf's Politics', he uses his influence and wisdom to protect Naruto from being used as a political pawn.
Minato would likely be extremely shocked. Naruto is his son, and the idea of Naruto attacking him would be completely unexpected. He would probably try to talk to Naruto first, to find out what is wrong and why he is being attacked.
One common ability is their speed. Minato was known as the Yellow Flash for his incredible speed. Naruto, with his Sage Mode and later forms, can also move extremely fast. Another is their use of the Rasengan. Minato created the Rasengan, and Naruto has mastered it and even developed it further.
One possible reason could be for Naruto's protection. Maybe Minato knew of some great danger that was coming for Naruto and he thought that banishing him would keep him out of harm's way. Another reason might be related to some prophecy or hidden power within Naruto that Minato feared could be misused if Naruto stayed in the village.