He might be angry at first. Naruto has grown up alone and had to fight for acceptance. So when his parents say they regret abandoning him, he could lash out, saying it's too late. After all, he has already faced so much without them.
I recommend "The Peasant Daughter-in-law". The female protagonist of this book also raised a child alone, while the male protagonist was the eldest young master of a peasant family. The plot also involved the situation where the female lead avoided certain people in order to protect her child. The entire novel was set in business and farming, telling the story of how the female protagonist started her own career and found true love. I hope you like my recommendation, Mwah~
The son could ask for some time and space if he feels too overwhelmed in the moment. Then, when he's ready, he can sit down with his parents and have a proper conversation. He can also share some educational resources about homosexuality with his parents to help them understand better.
In some fanfictions, Naruto may become extremely bitter. He could feel a deep sense of betrayal and this might fuel his determination to become stronger, not for the sake of the village at first, but more for self - vindication. He might isolate himself from others and struggle with his identity.
One possible reason could be that Naruto has some sort of power within him that they fear. Maybe it's a power that they don't understand and think could be dangerous, so they hate him out of fear.
Inosuke survives throughout the manga. The story doesn't have his death as part of the plot. His character remains active and plays a significant role until the end.