This seems to be sincere, and it is altogether a nice message.
Publicly asking for forgiveness is direct proof that someone lives in a guilt culture, where people take personal responsibility for their actions.
We've noted here many times that the Arab and Muslim worlds live with a different mindset, the honor/shame culture. where what you do it not as important as what others think you do. Your own actions are not relevant.
So how do Arabs look at this message from Zuckerberg?
In Al Quds al Arabi, this message is called an "embarrassing situation" for Zuckerberg! A person who publicly admits mistakes is a person who is shaming himself in public, in the honor/shame world.
The very thing that helps people improve themselves - looking honestly at themselves and trying to learn from mistakes - is anathema to most people who grew up in honor/shame societies, where the primary concern is not to put yourself down but to puff yourself up for appearances sake. The idea of a public apology sounds insane to those in the shame culture. The apology itself is shameful, whether or not it is warranted.
Between Zuckerberg's tweet and Al Quds al Arabi's response, you can learn a great deal about the difference between Arabs and even the most assimilated Jews.