I fully agree with @Brobb.
In addition, why exactly do players argue in the ingame chat in your alliance? Do you not have other means of communication, a chat app such as Line? Then players who disagree can take their argument to PN. And be told to do so, if they happen to start an argument in the ingame chat.
To my mind, arguing in ingame chat, in front of everybody, is
a. very bad manners indeed (you do not wash dirty laundry in public)
b. a symptom of the fact that there are no other forms of communication for your alliance members.
The only argument that I ever had in ingame chat was with an arrogant little macho jerk who steadfastly refused to install Line, even after the ally leader repeatedly requested that he do so.
With no other means of communication - and after repeated insults by that macho jerk to me, for the simple reason that I am a a woman - we battled it out in ingame chat. Oh, did we ever! The jerk left a few days later, of his own accord. - Had the leader banned me from the chat for not suffering insults in silence, I would have left immediately, without ever looking back.
Long story short:
Ask your members to install another means of online communication, such as Line. And I think that such problems will solve themselves.