Is it ethical for entrepeneurs such as Musk and Zuckerberg to engage in quarrels in social networks?

They're private individuals so they can do whatever they want. Although I'd say it requires some wisdom to figure out if your behavior is hurting your company significantly or not.

Nowadays everything is about PR and hype and nothing else.

My opinion about this situation is that such behavior is unethical for such successful entrepreneurs as Musk and Zacherberg. Individual disagreements and discussions can be useful for public dialogue, but engaging in frank disputes and even planning a fight in mixed martial arts (MMA) supports violence in sports and aggression. Such behavior does not correspond to the image of great businessmen and can have a negative impact on their reputation and brand. Instead, they should use their influence and resources to promote positive values and solve social problems. Of course, it can be taken into account that entrepreneurs, as individuals, have a personal life, and they should be allowed to express their opinions freely. They may argue that participation in public disputes or in events such as MMA fights is a form of self-expression and should not be considered as a reflection of their professional duties or ethical norms, but still their large presence on social media should require being more careful in choosing PR strategies, and avoiding such moments and events