They finally added this long awaited feature in the game with patch 9.14.
>Show [Allied] Chat
We've added a new option under Settings>Interface>Chat that will now allow you to mute your allies' chats. There is now a separate checkbox for "Show [Allied] Chat" next to the already existing "Show [All] Chat". Both settings will be checked by default, but players can now uncheck both to mute both enemies' and teammates' chats permanently, or until they're turned back on. However, unchecking both will not mute the pre- and post-game chat, but we've heard your requests and are considering including those in the future!
I don't know if i will use this feature, but i know there are a lot of people who want to use it. I just wish the game would notify all players in the team when someone is using this feature so they don't get triggered when that person doesn't respond to them.