Cap would be shocked at first. He trusts his comrades, and for the Clint team to betray him would be unexpected. He would likely feel a sense of betrayal and anger. He might start by trying to isolate the situation, to keep the knowledge of the betrayal from causing too much unrest in the Avengers. Then he would try to find a way to stop the Clint team from causing more harm, whether through negotiation or combat.
Well, it could be that the Clint team betrays Cap for some personal gain. Perhaps they are offered something really valuable like a powerful weapon or a chance to bring back a lost loved one. They then turn against Cap, which would make for a very tense and action - filled story. Cap would have to figure out how to deal with this betrayal, either by trying to reason with them or fighting them if necessary.
In the long run, Percy might grow from the experience. He could become more cautious in his relationships and less trusting. Or, if there's a chance for redemption in the fanfic, he might be open to forgiving Annabeth if she shows true remorse and has a valid reason for her actions. But initially, it would be a very difficult and emotional time for him.
Issei would probably first try to understand why Rias has betrayed him. If he finds out that she was forced or manipulated, he might try to save her. But if it was a conscious choice, he could become angry and vow revenge. He has a strong will, and this betrayal could fuel his determination to become stronger on his own.
At first, Naruto would likely be extremely shocked. He has always considered Sakura a friend and teammate, so this would be a huge blow. He might question his own judgment in trusting her.
At first, Percy would likely be angry. He has faced so many challenges with the belief that his father was on his side. The betrayal would make him feel like all his efforts were in vain. He could lash out, perhaps even using his powers in a more reckless way. But as time goes on, he might start to question if there's a deeper reason behind Poseidon's actions and try to find out the truth, especially if he still has friends who believe in him and encourage him to look deeper.
Percy would be extremely hurt. Sally is his mother, and her betrayal would shatter his world. He might initially go into denial, not wanting to believe that she could do such a thing.
However, Naruto also has a big heart. In the long run, he would probably try to find a way to save Kakashi or bring him back to the right side. He wouldn't give up on Kakashi easily, believing that there must be some underlying reason for his actions and that he can be redeemed.
Naruto would likely be initially shocked. He has always considered the Kyubii as a part of him and a friend in some ways. So the betrayal would be a huge blow to his sense of trust.
Pikachu might be very confused. Since Pikachu is Ash's closest companion, it would be torn between loyalty to Ash and the sense that what Ash did to Tyson was wrong. It might try to communicate with Ash to make him see his mistake.
Naruto could also feel a sense of confusion. He might wonder what he did wrong or what made Fem Kyuubi choose Sasuke over him. This confusion could lead him to question his own worth and his relationships with others. However, in true Naruto fashion, he would eventually rise above these negative feelings and focus on his goals, like protecting the village and his friends.