Any clan member can be added to your Ignore list and you won't ever see this user's messages again. Just tap/click on one of this player's messages, then select Ignore and the user's messages won't be visible in your clan chat.
If you ever change your mind, adding them back is just as simple: go to the clan chat settings, select the Ignore List tab and clear the mark next to your fellow player's nickname. The user's messages will show up in the chat once again.
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