Hello Hazem, how have you been?
The word/noun "brawl" means a physical fight, a rough, physical, beating each other, fight. The phrase "bar brawl" means some drunken fight in a bar. As you sometimes see, for example, in Western (cowboy) movies, where the people get drunk in a bar and begin fighting and wreck the place--tables, chairs, etc.
In your example, they are using the phrase or the image of a "bar brawl" to describe some of the vicious VERBAL fighting that takes places in social media, FaceBook, etc, over different volatile issues in the world today.
As always my friend, best wishes in your language studies and write me if you have more questions or if my comments are unclear.