I'm not sure what iOS 7.1 has in store (we're writing this at a time when only betas have been released) as regards turning off group message notifications, but this is one of the most annoying features of iOS 7.That you can't mute or leave a Group Message is kind of ridiculous.
Given the popularity of group messaging in apps like Whatsapp, it seems obvious why Apple added that feature but they did a lousy job. I do hope jailbreak community comes up with a way to turn off / mute group notifications but till then, here are two workarounds that might work for you.
The Less-Likely Workaround: Blocking People
Suppose two or three of your friends are talking about something that you are not even remotely interested in, and you want to leave the group message. iOS 7 doesn't let you do that now.
If it doesn't hurt much, you can temporarily block the contacts to stop receiving any group message. Here's how to block contacts.
The downside to this is that you will not receive any individual messages, calls or FaceTime calls from these blocked people. Too bad a workaround if you are expecting them to call/text you.
The Other Workaround: Mute Message Notifications
The only sane workaround till Apple fixes the Group Message issue is to turn off notifications from Message app. When you turn off notifications, all alerts from the Message app are muted. So, if there's a conversation going on in some group message thread, you will get them, but you won't be disturbed by any alert. You can tweak this workaround in many ways.
Do this to Turn off Group Messages in iOS 7:
- Go to Settings → Notification Center → Messages
- Switch the Alert Style to None.
- Tap on Alert Sound and select None.
- Let the Badge App Icon be ON so that when you look at your iPhone, your attention is drawn to the Message app (so you can check for other messages occasionally).
- Additionally, you can turn off Show in Notification Center and Show on Lock Screen.
As you can see, this is just a workaround (a very silly but functional one). It doesn't prevent the group messages from crowding your Message app. But it prevents your phone from going ‘ding' every time there's a new group message that you don't even want to see.