Boruto's strength in the manga is considerable. He's developed new jutsus and strategies, and has overcome many tough challenges. His potential keeps increasing as the story progresses.
He may try to understand Boruto's reasons. Naruto has always been one to look for the good in people. So, even when hurt, he might give Boruto the chance to explain himself. He could say something like 'Boruto, I know you didn't mean it. Let's talk about what's wrong.' He'll be patient and try to resolve the issue rather than getting angry right away.
In the fanfic, when Kushina realizes Naruto is gone, she might first be in a state of shock. She could then start searching everywhere for him, frantically asking people if they've seen him. Maybe she'll recall their last moments together and feel a deep sense of regret for not being more careful with him.
Kakashi could be initially shocked. He might not have expected Naruto to have such feelings towards him. But being Kakashi, he would probably handle it in a calm and collected manner.
They could start by having an honest conversation. Naruto could sit down with Boruto and just listen to his fears without judgment. This would be a first step in building a better relationship.
He might be initially confused. Naruto is a character full of energy and he would probably just start blabbing about how he is a boy, not a girl. He could get a bit frustrated as well because Naruto doesn't like being misunderstood.
Boruto's reaction would be complex. He'd be heartbroken, for sure. He might start to question his own worth and purpose. But over time, he'd realize that he has to carry on Naruto's legacy. He'd become more serious and focused. He'd also become more empathetic towards others, understanding the weight of sacrifice. He might even start to study Naruto's techniques and leadership style more closely, trying to emulate the things that made Naruto such a great Hokage and hero.