Harry would likely be angry. He has always been a fighter. He might see it as an unjust act and decide to fight back against the decision. He could try to find evidence to clear his name. He might also feel a sense of betrayal, especially if his friends in Gryffindor don't immediately stand up for him. He would then have to figure out where he belongs in Hogwarts without the Gryffindor identity.
He'd probably be devastated at first. Gryffindor has been his home at Hogwarts, and his friends are there. But he's also a resilient character. He might start to question the fairness of the banishment and try to prove his innocence. He could look for allies outside of Gryffindor, like Luna from Ravenclaw, who might believe in him.
In some fanfictions, Harry could become withdrawn and depressed at first. Losing his place in Gryffindor is like losing his family. But then, he might find new strength and purpose, perhaps by joining forces with some outcasts in the wizarding world and forming a new group that challenges the unjust actions of Gryffindor house.
He would probably be extremely hurt. Gryffindor was like his family at Hogwarts, so being exiled would be a huge blow. He might initially feel angry and betrayed.
Harry would probably be deeply hurt. He has always considered Gryffindor his home in Hogwarts, so such a betrayal would be a huge blow to him. He might initially be in disbelief and try to find out the truth.
In some fanfictions, it could be a political move within Hogwarts. There might be a group that wants to undermine Dumbledore's influence, and since Harry is so closely associated with him, they target Harry by getting him banished from Gryffindor. This could also be related to the discovery of some long - hidden secret about Harry's family that makes the Gryffindors view him differently.
Another reason could be related to a new prophecy. Suppose a new prophecy emerged that said Harry Potter's presence in Gryffindor would bring great danger to the house. The Gryffindor students and faculty, believing in the importance of protecting the whole house, might have decided to banish him. But of course, this would be a very difficult decision as Harry has been an important part of Gryffindor before. And in the end, the prophecy might turn out to be misinterpreted.
He might become more independent. Without the support of Gryffindor, he has to rely solely on himself. So he becomes more self - reliant and his decision - making skills improve.
Well, at first, most of Harry's Gryffindor friends would be taken aback. They have always had a certain animosity towards Slytherin. But as time goes on, if they see that the Slytherin Harry is betrothed to is kind - hearted and doesn't hold the same prejudices as some of the other Slytherins, they might start to come around. For instance, Seamus might start to joke around with the Slytherin, and Dean could start to include them in group activities. It would be a slow process of acceptance as they get to know the Slytherin better through Harry.
In some fanfictions, it could be due to a misunderstanding. Maybe someone framed Harry for a serious rule violation that Gryffindor's house values highly, like cheating in an important magical exam. And the evidence against him seems so strong that the Gryffindor house decides to banish him.
He might be surprised. The Harry Potter world has its own set of rules and characters that are very different from what Merlin is used to in his Arthurian world.
He'd probably be annoyed. Snape is a serious wizard and he might think fanfiction is a silly Muggle - influenced concept.