As you know, if you are in a clan, they can send clan messages to every member of the clan, giving them a notification in their inbox.
There should be a way to disable notifications for clan messages without leaving the clan itself.
if not that, Give a seperate notification for when you recieve one; like "You just got a clan message!" and its like every other notif, you click the text and itll direct you to the message and which clan it was sent from.